2 次 (拡大) 体の類数の可除性および非可除性に関する文献 (2-part のみに関するものは除く)

(2012 年 3 月更新版)

[1] T. Nagell : Über die Klassenzahl imaginär quadratischer Zahkörper, Abh. Math. Sem. Univ. Hamburg 1 (1922), 140–150; DOI: 10.1007/BF02940586 [m6382u5527561814.pdf (417.0 KB)]; reprinted in Collcted Papers of Trygve Nagell (P. Ribenboim, ed.), Queen’s Papers in Pure and Applied Mathematics, Volume 121, Queen’s Univ., Kingston, ON, Canada, 2002, Volume 1, 17, pp. 197–209; JFM 48.0170.03 (reviewed by Hecke) [html, DVI, ps, PDF, TeX].

[2] P. Humbert : Sur les nombres de classes de certains corps quadratiques, Comment. Math. Helv. 12 (1939), 233–245; DOI: 10.1007/BF01620650 [v7j912m7k73l76v7.pdf (471.1

KB)]; comahe-001_1939-1940_12_a_016_d.pdf, SEALS;
PPN358147735_0012_log19.pdf (854,52 KB), GDZ; [PDF],

DigiZeitschriften; MR0002359 (2, 39b) (reviewed by H. W. Brinkmann; reprinted in Reviews in Number Theory, volume 5, R14-1) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0023.10401 (reviewed by H. Brandt) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 66.0119.01 (reviewed by W. Neuhaus) [html, DVI, ps, PDF, TeX].

[3] P. Humbert : Note relative à l’article: Sur les nombres de classes de certains corps quadratiques, Comment. Math. Helv. 13 (1940), 67; DOI: 10.1007/

BF01378052 [q5075521t054m651.pdf (36.4 KB)]; comahe
-001_1940-1941_13_a_006_d.pdf, SEALS; PPN358147735

_0013_log9.pdf (59,91 KB), GDZ; [PDF], DigiZeitschriften; MR0003655 (2, 250d) (reviewed by H. W. Brinkmann; reprinted in Reviews in Number Theory, volume 5, R14-2) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0024.01001 (reviewed by H. Brandt) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 66.0120.01 (reviewed by W. Neuhaus) [html, DVI, ps, PDF, TeX].

[4] M. Gut : Kubische Klassenkörper über quadratischimaginären Grundkörpern, Nieuw Arch. Wiskunde (2) 23 (1951), 185– 189; MR0043827 (13, 524d) (reviewed by C. Chevalley; reprinted in Reviews in Number Theory, volume 5, R14-15) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0043.04203 (reviewed by H. Bergström) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[5] M. Gut : Relativquadratische Zahlkörper, deren Klassenzahl durch eine vorgegebene ungerade Primzahl teilbar ist, Comment. Math. Helv. 28 (1954), 270–277; DOI: 10.1007/BF02566933 [11521h4750588072.pdf (259.5 KB)];

comahe-002_1954_28_a_013_d.pdf, SEALS; PPN358147735_

0028_log17.pdf (486,76 KB), GDZ; [PDF], Digi-Zeitschriften; MR0066427 (16, 573f) (reviewed by C. Chevalley; reprinted in Reviews in Number Theory, volume 5, R14-29) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0058.03103 (reviewed by Z. Suetuna) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[6] M. Gut : Relativquadratische Zahlkörper, deren Klassenzahl durch eine vorgegebene ungerade Primzahl teilbar ist, Proceedings of ICM (Amsterdam, 1954), Vol. II, North-Holland,

Amsterdam, 1954, p. 26; icm1954.2.0026.0026.ocr.djvu
(52 K), icm1954.2.0026.0026.ocr.pdf (100 K), IMU.

[7] N. C. Ankeny and S. Chowla : On the divisibility of the class number of quadratic number fields, Pacific J. Math. 5 (1955), No. 3, 321–324; euclid.pjm/1103044454 [PDF (257 KB), DjVu (67 KB)]; reprinted in The collected papers of Sarvadaman Chowla, Volume II (J. G. Huard and K. S. Williams, eds.), Univ. Montreal, Les Publications CRM, Montreal, QC, 1999, 203, pp. 842–845; MR0085301 (19, 18f) (reviewed by C. Arf; reprinted in Reviews in Number Theory, volume 5, R14-35)

[html, PDF, DVI, PostScript, BibTeX]; Zbl 0065.02402 (reviewed by Z. Suetuna) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[8] S.-N. Kuroda : On the class number of imaginary quadratic number fields, Proc. Japan Acad. [日本學士院紀要] 40 (1964), No. 6, 365–367; doi:10.3792/pja/1195522712, euclid.pja/1195522712 [PDF (278 KB)]; JOI:JST.Journal archive/pjab1945/40.365 [40_365.pdf (259 K)], Journal @rchive, JST; doi:10.3792/pja/1195522712, MR0170882 (30 #1117) (reviewed by K. Grant; reprinted in Reviews in Number Theory, volume 5, R14-48) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0128.03404 (reviewed by E. Maus) [scanned image].

[9] C. S. Herz : Construction of class fields, Seminar on complex multiplication. Seminar held at the Institute for Advanced study, Princeton, N. J., Lecture Notes in Math., vol. 21, Chap. VII, Springer-Verlag, New York and Berlin, 1966, 21 pp.; DOI: 10.1007/BFb0091557 [1131h3227215v01j.pdf (840.8 KB)]; Zbl 0147.03902 (reviewed by E. Maus) [scanned image].

[10] A. Yokoyama : On the relative class number of finite algebraic number fields, J. Math. Soc. Japan [日本数学会欧文誌] 19 (1967), No. 2, 179–184; doi:10. 2969/jmsj/01920179, euclid.jmsj/1260478687 [PDF (618 KB)]; JOI:JST.Journalarchive/jmath1948/19.179 [19_179. pdf (507 K)], Journal@rchive, JST; MR0210685 (35 #1571) (reviewed by T. Kubota; reprinted in Reviews in Number Theory, volume 5, R26-33) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 0154.30402 (reviewed by J. Browkin) [scanned image].

[11] T. Honda : On real quadratic fields whose class numbers are multiples of 3, J. Reine Angew. Math. 233 (1968), 101–102; doi: 10.1515/crll.1968.233.101 [PDF (274 KB)];

PPN243919689_0233_log8.pdf (140,08 KB), GDZ; [PDF], Di-

giZeitschriften; MR0236144 (38 #4442) (reviewed by T. Kubota; reprinted in Reviews in Number Theory, volume 5, R14-78) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0165.06501 (Autorreferat) [scanned image].

[12] Y. Yamamoto : On unramified Galois extensions of quadratic number fields, Osaka J. Math. 7 (1970), no. 1, 57–76; euclid.ojm/1200692686 [PDF (1592 KB)]; ojm07_01_04.pdf, URL: http://ir.library.osaka-u.ac.jp/meta-bin/mt-pdetail.cgi ?smode=1&edm=0&tlang=1&cd=00030553; MR0266898 (42 #1800) (reviewed by J. B. Kelly; reprinted in Reviews in Number Theory, volume 5, R14-96) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0222.12003 (reviewed by H. Yokoi) [scanned image].

[13] D. Shanks : New types of quadratic fields having three invariants divisible by 3, J. Number Theory 4 (1972), no. 6, 537–556; doi:10.1016/0022-314X(72)90027-3 [PDF (783 K)]; MR0313220 (47 #1775) (reviewed by T. Metsänkylä; reprinted in Reviews in Number Theory, volume 5A, R14-213) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0265.12001 (Autorreferat) [scanned image].

[14] D. Shanks and P. J. Weinberger : A quadratic field of prime discriminant requiring three generators for its class group, and related theory, Acta Arith. XXI (1972), 71–87; aa21139.pdf, icm; MR0309899 (46 #9003) (reviewed by T. Lepistö; reprinted in Reviews in Number Theory, volume 5A, R14-211) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0249.12010 (reviewed by O. Neumann) [scanned image].

[15] S. Chowla and P. Hartung : Congruences for class-numbers of imaginary quadratic fields (mod 3), Norske Vid. Selsk. Skr. (Trondheim) 1972, no. 12, 2 pp.; reprinted in The collected papers of Sarvadaman Chowla, Volume III (J. G. Huard and K. S. Williams, eds.), Univ. Montreal, Les Publications CRM, Montreal, QC, 1999, 304, pp. 1211–1212; MR0332718 (48 #11044) (reviewed by J. V. Armitage; reprinted in Reviews in Number Theory, volume 5A, R14-232) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0242.12006 (Zusammenfassung der Autoren) [scanned image].

[16] P. J. Weinberger : Real quadratic fields with class number divisible by n, J. Number Theory 5 (1973), no. 3, 237–241; doi:10.1016/0022-314X(73)90049-8 [PDF (184 K)]; MR0335471 (49 #252) (reviewed by T. Lepistö; reprinted in Reviews in Number Theory, volume 5A, R14-234) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0287.12007 (Aus der Einführung) [scanned image].

[17] M. Craig : A type of class group for imaginary quadratic fields, Acta Arith. XXII (1973), fasc. 4, 449–459. (errata insert); aa2246.pdf, icm; MR0318098 (47 #6647) (reviewed by T. Metsänkylä; reprinted in Reviews in Number Theory, volume 5A, R14-219) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0227.12003 (Autorreferat) [scanned image]; Correction in [29].

[18] D. Shanks and R. Serafin : Quadratic fields with four invariants divisible by 3, Math. Comp. 27 (1973), no. 121, 183–187; DOI: 10.1090/S0025-5718-1973-0330097-0 [PDF]; doi:10.2307/2005260 [PDF (148 KB)], JSTOR; MR0330097 (48 #8436a) (reviewed by H. Cohn; reprinted in Reviews in Number Theory, volume 5A, R14-229) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0252.12001 (Zusammenfassung der Autoren) [scanned image]; Corrigenda: ibid. 27 (1973), no. 124, 1012; DOI: 10.1090/S0025-5718-1973-0330098-2 [PDF]; doi:10.2307/2005552 [PDF (128 KB)], JSTOR; MR0330098 (48 #8436b) (reviewed by H. Cohn; reprinted in Reviews in Number Theory, volume 5A, R14-229) [html, PDF, DVI, PostScript, BibTeX].

[19] O. Neumann : Relativ-quadratische Zahlkörper, derem Klassenzahlen durch 3 teilbar sind, Math. Nachr. 56 (1973), Issue 1-6, 281–306; DOI: 10.1002/mana.19730560128 [PDF (1072 K)]; MR0327714 (48, #6056) (reviewed by J. Browkin; reprinted in Reviews in Number Theory, volume 5A, R14-228) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0268.12002 (Autorreferat) [scanned image].

[20] S. Chowla and P. Hartung : Congruence properties of class numbers of quadratic fields, J. Number Theory 6 (1974), no. 2, 136–137; doi:10.1016/0022-314X(74)90052-3 [PDF (50 K)]; reprinted in The collected papers of Sarvadaman Chowla, Volume III (J. G. Huard and K. S. Williams, eds.), Univ. Montreal, Les Publications CRM, Montreal, QC, 1999, 311, pp. 1228–1229; MR0332719 (48 #11045) (reviewed by J. S. Joel; reprinted in Reviews in Number Theory, volume 5A, R14-233) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0276.12008 (Zusammenfassung des Autors) [scanned image].

[21] P. Hartung : Proof of the existence of infinitely many imaginary quadratic fields whose class number is not divisible by 3, J. Number Theory 6 (1974), no. 4, 276–278; doi:10.1016/0022-314X(74)90022-5 [PDF (92 K)]; MR0352040 (50 #4528) (reviewed by P. J. Weinberger; reprinted in Reviews in Number Theory, volume 5A, R14-245) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0317.12003 (reviewed by R. Bölling) [scanned image].

[22] P. Hartung : Explicit construction of a class of infinitely many imaginary quadratic fields whose class number is divisible by 3, J. Number Theory 6 (1974), no. 4, 279–281; doi:10.1016/0022-314X(74)90023-7 [PDF (120 K)]; MR0352041 (50 #4529) (reviewed by P. J. Weinberger; reprinted in Reviews in Number Theory, volume 5A, R14-245E) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0317.12002 (reviewed by R. Bölling) [scanned image].

[23] C. Neild and D. Shanks : On the 3-rank of quadratic fields and the Euler product, Math. Comp. 28 (1974), no. 125, 279–291; DOI: 10.1090/S0025-5718-1974-0352042-5 [PDF]; doi:10.2307/2005835 [PDF (296 KB)], JSTOR; MR0352042 (50 #4530) (reviewed by T. Lepistö; reprinted in Reviews in Number Theory, volume 5A, R14-246) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0277.12005 (Autorreferat).

[24] �� �� ������ ���� � : ������������� ����� ����������

���� Colloq. Math. XXXII (1974-1975), Fasc. 2, 291–300; MR0382228 (52 #3113) (reviewed by J. Browkin; reprinted in Reviews in Number Theory, volume 5A, R14-258) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0277.12004 (Autorreferat).

[25] F. Diaz y Diaz : Sur les corps quadratiques imaginaires dont le 3-rang du groupe des classes et supérieur à 1, Séminaire Delange-Pisot-Poitou, 15e année (1973/74), Théorie des nombres, Fasc. 2, Exp. No. G15, 10 pp. Secrétariat

                                                            Math., Paris, 1975; SDPP_1973-1974__15_2_A10_0.djvu,
                                                            SDPP_1973-1974__15_2_A10_0.pdf, Numdam; MR0392909

(52 #13722) (reviewed by W. Johnson; reprinted in Reviews in Number Theory, volume 5A, Y40-215) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0323.12007 (reviewed by R. Bölling) [scanned image].

[26] D. Shanks : Class groups of the quadratic fields found by F. Diaz y Diaz, Math. Comp. 30 (1976), no. 133, 173–178; DOI: 10.1090/S0025-5718-1976-0399039-9 [PDF]; doi:10.2307/2005441 [PDF (162 KB)], JSTOR; MR0399039 (53 #2890) (reviewed by T. Metsänkylä; reprinted in Reviews in Number Theory, volume 5A, R14-266) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0333.12005 (reviewed by R. Bölling) [scanned image]; Corrigendum : ibid. 30 (1976), no. 136, 900; DOI: 10.1090/S0025-5718-1976-0406968-6 [PDF]; doi:10.2307/2005421 [PDF (106 KB)], JSTOR; MR0406968 (53 #10753) (reprinted in Reviews in Number Theory, volume 5A, R14-268E) [html, PDF, DVI, PostScript, BibTeX].

[27] C. Queen : A note on class number of imaginary quadratic fields, Arch. Math. (Basel) 27 (1976), No. 3, 295–298; DOI: 10.1007/BF01224674 [uv2t75r00731873n.pdf (148.9 KB)]; MR0406976 (53 #10760) (reviewed by C. J. Parry; reprinted in Reviews in Number Theory, volume 5A, R14-271) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0334.12008 (reviewed by R. Bölling) [scanned image].

[28] R. Bölling : Über den 3-Rang von quadratischen Zahlkörper und den Rang gewisser elliptischer Kurven, Math. Nachr. 73 (1976), 155–170; DOI:10.1002/mana.19760730113 [PDF (650 K)]; MR0600811 (82d:12002) (reviewed by L. D. Olson; reprinted in Reviews in Number Theory, volume 2A, G05-278) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0357.12005 (reviewed by Lepistö) [scanned image].

[29] 棚橋勝美 [Tanahashi, K.] : ある種の実 2 次体の類数について, 数論的関数の特性 [Characters of Number-Theoretic Functions] (京都大学数理解析研究所, 1975) (山本幸一編), 数理解析研究所講究録 [RIMS Kokyuroku] 274, 1976, 108–131; 0274-12.pdf; 0274-12.pdf (1.73 MB), URI: http://hdl.handle.net/2433/105970; MR0453693 (56 #11953) (reviewed by A. Takaku; reprinted in Reviews in Number Theory, volume 5A, R14-295) [html, PDF, DVI, PostScript, BibTeX].

[30] 中原徹 [Nakahara, T.] : イデアル類群が 3-及び 5-部分群をもつ実二次体について, 数論的関数の特性 [Characters of Number-Theoretic Functions] (京都大学数理解析研究所, 1975) (山本幸一編), 数理解析研究所講究録 [RIMS Kokyuroku] 274, 1976, 132–147; 0274-13.pdf; 0274-13.pdf (1.01 MB), URI: http://hdl.handle.net/2433/105969; MR0476697 (57 #16256) (reviewed by H. Yokoi; reprinted in Reviews in Number Theory, volume 5A, R14-300) [html, PDF, DVI, PostScript, BibTeX].

[31] M. Craig : A construction for irregular discriminants, Osaka J. Math. 14 (1977), no. 2, 365–402; euclid.ojm/1200770450 [PDF (2044 KB)]; ojm14_02_07.pdf, URL: http://ir.library.osaka-u.ac.jp/meta-bin/mt-pdetail.cgi ?smode=1&edm=0&tlang=1&cd=00030143; MR0450226 (56 #8522) (reviewed by P. Damey; reprinted in Reviews in Number Theory, volume 5A, R14-292) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0366.12007 (Autorreferat) [scanned image]; Correction : ibid. 15 (1978), no. 2, 461; euclid.ojm/1200771284 [PDF (254 KB)]; ojm15_02_15.pdf, URL: http://ir.library.osaka-u.ac.jp/meta-bin/mt-pdetail.cgi ?smode=1&edm=0&tlang=1&cd=00030193; MR0504302 (80a:12011) [html, PDF, DVI, PostScript, BibTeX] (reprinted in Reviews in Number Theory, volume 5A, R14-219E) [html, PDF, DVI, PostScript, BibTeX].

[32] C. J. Parry : Real quadratic fields with class numbers divisible by five, Math. Comp. 31 (1977), no. 140, 1019–1029; DOI: 10.1090/S0025-5718-1977-0498483-X [PDF]; doi:10.2307/2006134 [PDF (695 KB)], JSTOR; MR0498483 (58 #16593) (author’s summary; reprinted in Reviews in Number Theory, volume 5A, R14-306) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0394.12001 (reviewed by T. Lepistö) [scanned image].

[33] M. D. Hendy : Class number divisors for some real quadratic fields, Occasional Publications in Mathematics, No. 5. Department of Mathematics, Massey University, Palmerston North, 1977, i+3 pp.; MR0463138 (57 #3099) (reviewed by T. Metsänkylä; reprinted in Reviews in Number Theory, volume 5A, R14-298) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0392.12004 (reviewed by P. Draxl) [scanned image].

[34] F. Diaz y Diaz : On some families of imaginary quadratic fields, Math. Comp. 32 (1978), no. 142, 637–650; DOI: 10.1090/S0025-5718-1978-0485775-4 [PDF]; doi:10.2307/2006174 [PDF (1068 KB)], JSTOR; MR0485775 (58 #5582) (reviewed by E. Brown; reprinted in Reviews in Number Theory, volume 5A, R14-302) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0383.12005 (reviewed by T. Metsänkylä) [scanned image].

[35] C. J. Parry : On the class numbers of relative quadratic fields, Math. Comp. 32 (1978), no. 144, 1261–1270; DOI: 10.1090/S0025-5718-1978-0502013-4 [PDF]; doi:10.2307/2006350 [PDF (706 KB)], JSTOR; MR0502013 (80h:12004) (reviewed by S. P. Cemushkin; reprinted in Reviews in Number Theory, volume 5A, R26-263) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0401.12008 (reviewed by H. C. Williams) [scanned image].

[36] T. Nakahara : On real quadratic fields whose ideal class groups have a cyclic p-subgroup, Rep. Fac. Sci. Engrg. Saga Univ. Math. [佐賀大学理工学部集報. 数学] 6 (1978), 15–26; URI: http://portal.dl.saga-u.ac.jp/handle/123456789/13003; MR0490248 (80a:12005) (reviewed by G. J. Rieger; reprinted in Reviews in Number Theory, volume 5A, R14-309) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0402.12002 (reviewed by G. Gras) [scanned image].

[37] B. H. Gross and D. E. Rohrlich : Some results on the Mordell-Weil group of the Jacobian of the Fermat curve, Invent. Math. 44 (1978), fasc. 3, 201–224; DOI: 10.1007/BF01403161 [t114p426ul265001.pdf (860.8 KB)];

PPN356556735_0044_log19.pdf (1,50 MB), GDZ; [PDF], Di-

giZeitschriften; MR0491708 (58 #10911) (reprinted in Reviews in Number Theory, volume 2A, D44-252) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0369.14011 (reviewed by A. N. Paršin) [scanned image].

[38] F. Diaz y Diaz : Sur le 3-rang des corps quadratiques, Publ. Math. d’Orsay 78, 11, Université de Paris-Sud, Départment de Math., Orsay, 1978, vii+93 pp.; MR0532177 (80i:12005) (reviewed by V. Ennola; reprinted in Reviews in Number Theory, volume 5A, Y40-226E) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0405.12004 (reviewed by H. Cohn) [scanned image].

[39] R. Bölling : Bemerkungen über Klassenzahlen und Summen von Jacobi-Symbolen, Math. Nachr. 90 (1979), Issue 1, 159–172; DOI: 10.1002/mana.19790900113 [PDF (451 K)]; MR0550995 (81g:12008) (reviewed by L. Skula; reprinted in Reviews in Number Theory, volume 5A, R14-317) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0415.12003 (Autorreferat) [scanned image].

[40] F. Diaz y Diaz, D. Shanks and H. C. Willams : Quadratic fields with 3-rank equal to 4, Math. Comp. 33 (1979), no. 146, 836–840; DOI: 10.1090/S0025-5718-1979-0521299-4 [PDF]; doi:10.2307/2006320 [PDF (406 KB)], JSTOR; MR0521299 (80i:12004) (reviewed by T. Metsänkylä; reprinted in Reviews in Number Theory, volume 5A, Y40-226) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0409.12009 (Autorreferat) [scanned image].

[41] F. Diaz y Diaz : Quelques discriminants irreguliers, Proceedings of the sixth conference of Portuguese and Spanish mathematicians, Part II (Santander, 1979). Rev. Univ. Santander No. 2, part 2, (1979), pp. 753–758; MR0754781 (not reviewed); Zbl 0938.11503 (not reviewed).

[42] M. J. Cowles : On the divisibility of the class number of imaginary quadratic fields, J. Number Theory 12 (1980), no. 1, 113–115; doi:10.1016/0022-314X(80)90081-5 [PDF (113 K)]; MR0566877 (81m:12005) (reviewed by T. Nakahara; reprinted in Reviews in Number Theory, volume 5A, R14-318) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0427.12001 (reviewed by R. J. Stroeker) [scanned image].

[43] J.-F. Mestre : Courbes elliptiques et groupes des classes d’idéaux de certains corps quadratiques, Séminaire de théorie des nombres, 1979–1980, Exp. No. 15, Univ. Bordeaux I,

                                                            Talence, 1980, 18 pp.; PPN320141322_0009_log20.pdf (1,79

MB), GDZ; [PDF], DigiZeitschriften; MR0604213 (82j:12004) (reviewed by L. D. Olson; reprinted in Reviews in Number Theory, volume 5A, R14-329) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0442.12003 (reviewed by G. Henniart) [scanned image].

[44] K. Ohta : On algebraic number fields whose class numbers are multiples of 3, Bull. Fac. Gen. Ed. Gifu Univ. [岐阜大学教養部研究報告] 1981, no. 17, 51–54 (1982); MR0648342 (83h:12009) (reviewed by T. Lepistö; reprinted in Reviews in Number Theory, volume 5A, R26-283) [html, PDF, DVI, PostScript, BibTeX].

[45] R. J. Schoof : Class groups of complex quadratic fields, Math. Comp. 41 (1983), no. 163, 295–302; DOI: 10.1090/S0025-5718-1983-0701640-0 [PDF]; doi:10.2307/2007782 [PDF (863 KB)], JSTOR; MR0701640 (84h:12005) (reviewed by F. Diaz y Diaz; reprinted in Reviews in Number Theory, volume 5B, R11-604) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0516.12002 (reviewed by K. S. Williams) [scanned image].

[46] J.-F. Mestre : Courbes elliptiques et groupes des classes d’idéaux de certains corps quadratiques, J. Reine Angew. Math. 343 (1983), 23–35; doi: 10.1515/crll.1983.343.23 [PDF

                                                            (1714 KB)]; PPN243919689_0343_log5.pdf (1,37 MB), GDZ;

[PDF], DigiZeitschriften; MR0705875 (84m:12004) (reviewed by F. Diaz y Diaz; reprinted in Reviews in Number Theory, volume 5B, R29-620) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0502.12004 (Autorreferat) [scanned image].

[47] T. Uehara : On class numbers of imaginary quadratic and quartic fields, Arch. Math. (Basel) 41 (1983), No. 3, 256–260; DOI: 10.1007/BF01194836 [p67150v4hj752278.pdf (262.1 KB)]; MR0721057 (85e:11090) (reviewed by C. J. Parry; reprinted in Reviews in Number Theory, volume 5B, R29-635) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0532.12007 (reviewed by T. Lepistö) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[48] T. Uehara : Construction of certain real quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. [日本学士院紀要] 59 (1983), No. 8, 390–392; doi:10.3792/pjaa.59.390, euclid.pja/1195515412 [PDF (332 KB)]; MR0726532 (85b:11085) (reviewed by F. Diaz y Diaz; reprinted in Reviews in Number Theory, volume 5B, R11-610) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0538.12001 (reviewed by H. Yokoi) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[49] � 洪文 : �分数与�数及其他, 中国科学 A� 第 13 � (1983) 第 7 期 : 49–58; [CAJ, PDF], cnki; English translation : Lu, H. : The continued fractions, class number and the others, Sci. Sinica Ser. A XXVI (1983) No. 12, 1275–1284; [CAJ, PDF], cnki; MR0745799 (85i:11091) (reviewed by W. Johnson; reprinted in Reviews in Number Theory, volume 5B, R11-614) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0534.12003 (reviewed by K. S. Williams) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[50] J.-F. Mestre : Groupes des classes d’idéaux non cycliques de corps nombres, Seminar on number theory, Paris 1981–82 (Paris, 1981/82), Progr. Math., vol. 38, Birkhäuser Boston, Boston, Mass., 1983, pp. 189–200; MR0729168 (85m:11066) (reviewed by L. J. Federer; reprinted in Reviews in Number Theory, volume 5B, R11-617) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0533.12009 (reviewed by R. Gillard) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[51] � 洪文 [Lu, H.] : 一��二次域�数的可除性 [The divisibility of the class numbers of some real quadratic fields ], 数学学� 中文版 [Acta Math. Sinica] 第 28 � (1985) 第 6 期 : 756–762; [CAJ, PDF], cnki; MR0813328 (87c:11100) (reviewed by X. Zhang; reprinted in Reviews in Number Theory, volume 5B, R11-630) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0619.12002 (reviewed by Zhang X.) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[52] H. Naito : On the ideal class groups of totally imaginary quadratic extensions, J. Fac. Sci. Univ. Tokyo Sect. IA Math. [東京大学理学部紀要第 I 類 A 数学] 32 (1985), No. 2, 205–211; jfs320202.pdf (301 Kb), URI: http://hdl.handle.net/2261/6415; MR0802890 (86k:11057) (reviewed by J. Ritter; reprinted in Reviews in Number Theory, volume 5B, R11-624) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 0582.12004 (reviewed by D. Li) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[53] J. Nakagawa : Class numbers of quadratic extensions of algebraic number fields, Tôhoku J. Math. (2) [東北數學雑誌第二輯] 38 (1986), no. 2, 245–257; doi:10.2748/tmj/1178228491, euclid.tmj/1178228491 [PDF (1163 KB)]; 38_245.pdf (1198 K), Journal@rchive, JST; MR0843810 (87g:11146) (reviewed by F. Diaz y Diaz; reprinted in Reviews in Number Theory, volume 5B, R29-685) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0608.12009 (reviewed by Ch. Parry) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[54] R. A. Mollin : Diophantine equations and class numbers, J. Number Theory 24 (1986), no. 1, 7–19; doi:10.1016/0022-314X(86)90053-3 [PDF (675 K)]; MR0852186 (87i:11155) (reviewed by W. Johnson; reprinted in Reviews in Number Theory, volume 5B, R29-690) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 0591.12006 (reviewed by H. Yokoi) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[55] A. Hédi : Cycles canoniques d’idéaux réduits nombre des classes de certains corps quadratiques réels, Nagoya Math. J. 103 (1986), 127–132; euclid.nmj/1118780485 [PDF (344 KB)]; MR0858475 (87k:11117) (reviewed by F. Diaz y Diaz; reprinted in Reviews in Number Theory, volume 5B, R11-644) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0604.12005 (reviewed by R. Mollin) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[56] T. Uehara : On class numbers of cyclic quartic fields, Pacific J. Math. 122 (1986), No. 1, 251–255; euclid.pjm/1102702132 [PDF (448 KB), DjVu (96 KB)]; MR0825234 (87e:11129) (reviewed by K. Komatsu; reprinted in Reviews in Number Theory, volume 5B, R29-683) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 0659.12010 (reviewed by T. Lepistö) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[57] R. A. Mollin : On the class numbers of quadratic extensions of algebraic number fields, Proc. Japan Acad. Ser. A Math. Sci. [日本学士院紀要] 62 (1986), No. 1, 33– 36; doi:10.3792/pjaa.62.33, euclid.pja/1195514496 [PDF (440 KB)]; MR0839801 (87i:11156) (reviewed by I. Sh. Slavutskiĭ; reprinted in Reviews in Number Theory, volume 5B, R29-691) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0659.12009 (reviewed by T. Lepistö) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[58] J. Quer : Corps quadratiques de 3-rang 6 et courbes elliptiques de rang 12, C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), n^{∘} 6, 215–218; [PDF, JPEG, txt], Gallica; MR0907945 (88j:11074) (reviewed by R. Livné; reprinted in Reviews in Number Theory, volume 5B, R29-727) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0622.14025 (reviewed by H. G. Zimmer) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[59] H. Osada : Note on the class-number of the maximal real subfield of a cyclotomic field, Manuscripta Math. 58 (1987), fasc. 1–2, 215–227; DOI: 10.1007/BF01169091 [w76n211632w47q74.pdf (329.6 KB)];

                                                            PPN365956996_0058_log15.pdf (511,08 kB), GDZ; [PDF],

DigiZeitschriften; MR0884993 (88f:11106) (reviewed by R. Ernvall; reprinted in Reviews in Number Theory, volume 5B, R29-714) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0602.12002 [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[60] K. Horie : A note on basic Iwasawa λ-invariants of imaginary quadratic fields, Invent. Math. 88 (1987), fasc. 1, 31–38; DOI: 10.1007/BF01405089 [q533264371134276.pdf (338.5 KB)];

                                                            PPN356556735_0088_log8.pdf (599,56 KB), GDZ; [PDF],

DigiZeitschriften; MR0877004 (88i:11073) (reviewed by L. Washington; reprinted in Reviews in Number Theory, volume 5B, R11-651) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0585.12004 [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[61] � 茂� : 一�虚二次域�数的可除性, 科学通� [Kexue Tongbao] 第 32 � (1987) 第 10 期 : 724–727; [CAJ, PDF], cnki; MR0906592.

[62] P. Llorente and J. Quer : On the 3-Sylow subgroup of the class group of quadratic fields, Math. Comp. 50 (1988), no. 181, 321–333; DOI: 10.1090/S0025-5718-1988-0917838-7 [PDF]; doi:10.2307/2007934 [PDF (1183 KB)], JSTOR; MR0917838 (89b:11083) (reviewed by F. Diaz y Diaz; reprinted in Reviews in Number Theory, volume 5B, R11-666) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0639.12003 (reviewed by H. Cohn) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[63] F. Diaz y Diaz, P. Llorente and J. Quer : Cubic fields, a congruential criterion for Scholz’s theorem and new real quadratic fields with 3-rank equal to 4, Arch. Math. (Basel) 50 (1988), No. 4, 356–359; DOI: 10.1007/BF01190231 [x80211633v67053p.pdf (216.7 KB)]; MR0937339 (89d:11097) (reviewed by F. Halter-Koch; reprinted in Reviews in Number Theory, volume 5B, R29-741) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0642.12008 (reviewed by K. Lakkis) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[64] J. Nakagawa and K. Horie : Elliptic curves with no rational points, Proc. Amer. Math. Soc. 104 (1988), no.

1, 20–24; DOI: 10.1090/S0002-9939-1988-0958035-0 [PDF]; doi:10.2307/2047452 [PDF (156 KB)], JSTOR; MR0958035 (89k:11113) (reviewed by E. de Shalit; reprinted in Reviews in Number Theory, volume 5B, R45-614) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0663.14023 (reviewed by J. Silverman) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[65] K. Horie and Y. Ônishi : The existence of certain infinite families of imaginary quadratic fields, J. Reine angew. Math. 390 (1988), 97–113; doi: 10.1515/crll.1988.390.97

[PDF (1624 KB)]; PPN243919689_0390_log10.pdf (1,23

MB), GDZ; [PDF], DigiZeitschriften; MR0953679 (90e:11157) (reviewed by E. Nart; reprinted in Reviews in Number Theory, volume 5B, R11-695) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 0638.12001 (reviewed by K. Horie) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[66] 中川仁, 堀江邦明 [Nakagawa, J.; Horie, K.] : 有理点を持たない楕円曲線について, 代数的整数論–最近の種々の話題について– [Algebraic Number Theory -On Recent Topics-] (京都大学数理解析研究所, 1987) (佐武一郎編), 数理解析研究所講究録 [RIMS Kokyuroku] 658, 1988, 129–138 0658-12.pdf; 0658-12.pdf (499.69 kB), URI: http://hdl.handle.net/2433/100544.

[67] K. Horie : Trace formulae and imaginary quadratic fields, Math. Ann. 288 (1990), Heft 4, 605–612; DOI: 10.1007/BF01444553 [n14gl781l3r622n2.pdf (338.2 KB)];

PPN235181684_0288_log53.pdf (639,74 KB), GDZ; [PDF],

DigiZeitschriften; MR1081266 (91k:11099) (reviewed by B. Edixhoven; reprinted in Reviews in Number Theory, volume 5B, R29-810) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0692.12004 (reviewed by K. Horie) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[68] Le, M.-H. [� 茂�] : On the divisibility of the class number of the imaginary quadratic field ℚ(\sqrt{a^{2} − 4k^{n}}), Acta Math. Sinica (N. S.) 5 (1989), No. 1, 80–86; DOI: 10.1007/BF02107625 [l3k382k14150780u.pdf (278.2 KB)]; MR0998390 (90d:11117) (reviewed by K. S. Williams; reprinted in Reviews in Number Theory, volume 5B, R11-691) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0779.11053 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[69] � 茂� [Le, M.-H.] : �二次域 Q(\sqrt{1 + 4k^{2n}/a^{2}}) 的�数的可除性 [Divisibility of the class number of the real quadratic field Q(\sqrt{1 + 4k^{2n}/a^{2}})], 数学学� 中文版 [Acta Math. Sinica] 第 33 � (1990) 第 4 期 : 565–574; [CAJ, PDF], cnki; MR1081808 (91j:11090) (reviewed by K.-Q. Feng; reprinted in Reviews in Number Theory, volume 5B, R11-716) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0757.11034 (reviewed by Zhang, X.) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[70] T. Nakahara : A construction of quadratic fields whose class numbers are divisible by a power of 3, Number theory, Vol. II (Budapest, 1987), Colloq. Math. Soc. János Bolyai, 51, North-Holland, Amsterdam, 1990, pp. 889–897; MR1058250 (91i:11141) (reviewed by F. Diaz y Diaz; reprinted in Reviews in Number Theory, volume 5B, R11-715) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0704.11037 (reviewed by R. Mollin) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[71] H. Naito : Indivisibility of class numbers of totally imaginary quadratic extensions and their Iwasawa invariants, J. Math. Soc. Japan [日本数学会欧文誌] 43 (1991), No. 1, 185–194; doi:10.2969/jmsj/04310185, euclid.jmsj/1227108334 [PDF (1103 KB)]; JOI:JST.Journalarchive/jmath1948/43.185 [43_185.pdf (878 K)], Journal@rchive, JST; MR1082429 (92a:11131) (reviewed by K. Horie; reprinted in Reviews in Number Theory, volume 5B, R29-821) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0719.11072 (reviewed by H. Naito) [html, PDF, XML, ASCII, DVI, PS, BibTeX]; Erratum : ibid. 46 (1994), No. 4, 725–726; doi:10.2969/jmsj/04640725, euclid.jmsj/1227104610 [PDF (171 KB)]; JOI:JST.Journalarchive/jmath1948/46.725 [46_725.pdf (121 K)], Journal@rchive, JST; MR1291114 (95h:11122) (reviewed by K. Horie; reprinted in Reviews in Number Theory, volume 5B, R29-913) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0817.11048 [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[72] � �科 : �二次域理想�群的子群的决定, 科学通� [Kexue Tongbao] 第 36 � (1991) 第 24 期 : 1847–1849; [CAJ, PDF], cnki; 中国数学文摘 m92053823 [html]; English translation: Zhang X. : The determination of subgroups in ideal class groups of real quadratic fields, Chinese Sci. Bull. 37 (1992), no. 11, 890–893; [CAJ, PDF], cnki; Zbl 0762.11037 (reviewed by R. Mollin) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[73] J. J. Solderitsch : Quadratic fields with special class groups, Math. Comp. 59 (1992), no. 200, 633– 638; DOI: 10.1090/S0025-5718-1992-1139091-5 [PDF]; doi:10.2307/2153080 [PDF (176 KB)], JSTOR; MR1139091 (93a:11094) (reviewed by D. A. Buell; reprinted in Reviews in Number Theory, volume 5B, R29-842) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0773.11059 (reviewed by T. Lepistö) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[74] J.-F. Mestre : Corps quadratiques dont le 5-rang du groupe des classes est ≧ 3, C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), n^{∘} 4, 371–374; [PDF, JPEG, txt], Gallica; MR1179040 (93f:11076) (reviewed by H. Darmon; reprinted in Reviews in Number Theory, volume 5B, R29-858) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0763.11043 (reviewed by E. Nart) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[75] � 茂� [Le, M.-H.] : Baker 方法的若干�用 (�) [Applications of the Baker method (V)], �道科学与工程学� 第 10 � (1992) 第 1 期 : 73–77; [CAJ, PDF], cnki; 中国数学文摘 m93032117 [html].

[76] F. Leprévost : Courbes modulaires et 11-rang du corps quadratiques, Experiment. Math. 2 (1993), No. 2, 137– 146; euclid.em/1048516218 [PDF (228 KB), PostScript (NaN KB)]; leprevost.ps, ELibM, EMIS; MR1259427 (94m:11073) (reviewed by P. Satgé; reprinted in Reviews in Number Theory, volume 2B, G30-667) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0804.11062 (reviewed by R. Schoof) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[77] M.-H. Le : A Diophantine equation concerning on divisibility of the class number for some imaginary quadratic field, Indag. Math. (N. S.) 4 (1993), no. 1, 65–70; doi:10.1016/0019-3577(93)90052-Z; MR1213323 (94b:11111) (summary; reprinted in Reviews in Number Theory, volume 5B, R29-881) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0783.11011 (reviewed by R. P. Steiner) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[78] 曹珍富 [Cao, Z.-F.] : �于虚二次域�数的可除性 [Divisibility of the class numbers of imaginary quadratic fields ], 数学学� 中文版 [Acta Math. Sinica] 第 37 � (1994) 第 1 期 : 50–56; [CAJ, PDF], cnki; 中国数学文摘 m95010105 [html]; MR1272504 (95b:11104) (reviewed by M.-H. Le; reprinted in Reviews in Number Theory, volume 5B, R29-899) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0791.11057 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[79] 曹珍富 [Cao, Z.-F.] : �番�方程��二次域�数的可除性 [Diophantine equations and divisibility of the class numbers of the real quadratic fields ], 数学学� 中文版 [Acta Math. Sinica] 第 37 � (1994) 第 5 期 : 625–631; [CAJ, PDF], cnki; 中国数学文摘 m95054678 [html]; MR1311520 (96a:11119) (reviewed by X. Zhang; reprinted in Reviews in Number Theory, volume 5B, R29-921) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0823.11061 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[80] 内藤浩忠 : 総虚二次拡大体の相対類数, 整数論シンポジウム報告集 (香川大学, 1993) (伊藤博編), 1994, pp. 75–80.

[81] J. Brinkhuis : Normal integral bases and the Spiegelungssatz of Scholz, Acta Arith. LXIX (1995), fasc. 1, 1–9; aa6911.pdf, icm; MR1310838 (96a:11124) (reviewed by J.-F. Jaulent; reprinted in Reviews in Number Theory, volume 5B, R33-753) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0838.11073 (reviewed by J.-F. Jaulent) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[82] D. A. Buell and V. Ennola : On a parameterized family of quadratic and cubic fields, J. Number Theory 54 (1995), no. 1, 134–148; doi:10.1006/jnth.1995.1106 [PDF (491 K)]; MR1352641 (96h:11109) (reviewed by M. Olivier; reprinted in Reviews in Number Theory, volume 5B, R16-715) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0832.11039 (reviewed by R. Mollin) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[83] R. A. Mollin : Solutions of diophantine equations, and divisibility of class numbers of complex quadratic fields, Glasgow Math. J. 38 (1996), Part 2, 195– 197; doi:10.1017/S0017089500031438 [PDF (171 KB)]; MR1397175 (97h:11125) (reviewed by P. Stevenhagen) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0859.11058 (reviewed by F. Halter-Koch) [html, PDF, XML, ASCII, DVI, PS, Bib-TeX].

[84] Zhang, X, [� �科] and L. C. Washinton : Ideal class groups and their subgroups of real quadratic fields, Sci. China Ser. A 40 (1997), No. 9, 909–916; DOI: 10.1007/BF02878670 [d729721440781073.pdf (453.4 KB)]; MR1481686 (98j:11100) (reviewed by M. G. Leu) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 0907.11039 (reviewed by C. Parry) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[85] � 茂� [Le, M.-H.] : 一�有�虚二次域理想�群的指数� 番�方程 [An Exponential Diophantine equation concerning ideal class groups of imaginary quadratic fields ], 数学�志 [J. Math.] 第 17 � (1997) 第 1 期 : 69–71; [CAJ, PDF], cnki; 中国数学文摘 m98010124 [html].

[86] 曹珍富 [Cao, Z.-F.] : 虚二次域的�数与一��番�方程 [The class number of the imaginary quadratic field and some Diophantine equations ], 哈��工�大学学� [J. Harbin Inst. Technol.] 第 29 � (1997) 第 5 期 : 36–39; [CAJ, PDF], cnki; 中国数学文摘 m98044338 [html]; MR1613222 (99b:11118) (reviewed by X. Zhang) [html, PDF, DVI, PostScript, BibTeX].

[87] 袁平之 [Yuan, P.-Z.] : 也��二次域�数的可除性 [A talk about the divisibility of the class number of real quadratic fields ], 数学学� 中文版 [Acta Math. Sinica] 第 41 � (1998) 第 3 期 : 525–530; sxxb-98-41(3)-0525.pdf (377 KB); [CAJ, PDF], cnki; 中国数学文摘 m99021553 [html]; MR1640610 (99f:11145) (reviewed by S.-W. Zhang) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 1005.11058 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[88] Y. Kishi : A criterion for a certain type of imaginary quadratic fields to have 3-ranks of the class groups greater than one, Proc. Japan Acad. Ser. A Math. Sci. [日本学士院紀要] 74 (1998), No. 6, 93–97; doi:10.3792/pjaa.74.93, euclid.pja/1195509630 [PDF (505 KB)]; MR1644208 (2000a:11152) (reviewed by F. Lemmermeyer) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0930.11080 (reviewed by E. Benjamin) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[89] M. Sase : On a family of quadratic fields whose class numbers are divisible by five, Proc. Japan Acad. Ser. A Math. Sci. [日本学士院紀要] 74 (1998) No. 7, 120–123; doi:10.3792/pjaa.74.120, euclid.pja/1195509607 [PDF (425 KB)]; MR1658854 (2000b:11117) (reviewed by C. J. Parry)

[html, PDF, DVI, PostScript, BibTeX]; Zbl 0926.11081 (reviewed by M. Pohst) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[90] M. R. Murty : The ABC conjecture and exponents of class groups of quadratic fields, Number theory (Tiruchirapalli, 1996) (V. K. Murty and M. Waldschmidt, eds.), Contemp. Math., vol. 210, Amer. Math. Soc., Providence, R. I., 1998, pp. 85–95; MMR1478486 (98j:11098) (reviewed by A. Granville) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0893.11043 (reviewed by R. Mollin) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[91] 岸康弘 [Kishi, Y.] : 類数が 3 で割れる二次体の特徴付け, 代数的数論とその周辺 [Algebraic Number Theory and Related Topics] (京都大学数理解析研究所, 1997) (伊原康隆編), 数理解析研究所講究録 [RIMS Kokyuroku] 1026, 1998, 151–155; 1026-16.pdf; 1026-16.pdf (364.87 kB), URI: http://hdl.handle.net/2433/61760; MR1647363.

[92] 小松亨 : 実 2 次体の 3 次不分岐拡大について, 研究集会報告集 IX, 整数論 (早稲田大学, 1998) (足立恒雄編), 早稲田大学, 1998, pp. 10–19.

[93] K. Ono : Indivisibility of class numbers of real quadratic fields, Compositio Math. 119 (1999), no. 1, 1–11; doi:10.1023/A:1001533613223 [m007933q66170707.pdf (76.8 KB), Springer; S0010437X99000615a.pdf, CJO (78.5 KB)]; MR1711515 (2000i:11169) (reviewed by T. Metsänkylä) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1002.11080 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[94] É. Fouvry : Sur les propriétés de divisibilité des nombres de classes des corps quadratiques, Bull. Soc. Math. France

127 (1999), no. 1, 95–113; BSMF_1999__127_1_95_0.djvu,
BSMF_1999__127_1_95_0.pdf, Numdam;  MR1700470

(2000f:11145) (reviewed by D. R. Heath-Brown) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0993.11046 (reviewed by F. Lemmermeyer) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[95] W. Kohnen and K. Ono : Indivisibility of class numbers of imaginary quadratic fields and orders of Tate-Shafarevich groups of elliptic curves with complex multiplication, Invent. Math. 135 (1999), fasc. 2, 387–398; DOI: 10.1007/s002220050290 [wujkh4bjmk73kenu.pdf (131.3 KB)]; MR1666783 (2000c:11087) (reviewed by M. R. Murty) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0931.11044 (reviewed by R. Schoof) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[96] S. Wong : Elliptic curves and class number divisibility, Int. Math. Res. Not. 1999, No. 12, 661–672; DOI: 10.1155/S1073792899000343 [661.full.pdf]; MR1699211 (2000i:11088) (reviewed by K. Kramer) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0934.11032 (reviewed by J. A. Antoniadis) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[97] K. Belabas et E. Fouvry : Sur le 3-rang des corps quadratiques de discriminant premier ou presque premier, Duke Math. J. 98 (1999), No. 2, 217–268; DOI: 10.1215/S0012-7094-99-09807-1, euclid.dmj/1077228213 [PDF]; MR1695199 (2000i:11167) (reviewed by G. Greaves) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1061.11503 (reviewed by G. Greaves) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[98] J. H. Bruinier : Nonvanishing modulo l of Fourier coefficients of half-integral weight modular forms, Duke Math. J. 98 (1999), No. 3, 595–611; DOI: 10.1215/S0012-7094-99-09819-8, euclid.dmj/1077228361 [PDF]; MR1695803 (2000d:11061) (reviewed by B. Ramakrishnan) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0966.11019 (reviewed by G Köhler) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[99] D. Byeon : Class numbers and Iwasawa invariants of certain totally real number fields, J. Number Theory 79 (1999), no. 2, 249–257; doi:10.1006/jnth.1999.2433 [PDF (118 K)]; MR1728149 (2000j:11164) (reviewed by M. Yamagishi) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1012.11098 (reviewed by T. Metsänkylä) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[100] R. A. Mollin : Cyclic subgroups of ideal class groups in real quadratic orders, Glasg. Math. J. 41 (1999), Part 2, 197–206; doi:10.1017/S0017089599970799 [PDF (154 KB)]; MR1700025 (2000i:11164) (reviewed by L. Washington) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0990.11066 (reviewed by Zhang, X.) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[101] � 宏基 [Chen, H.] : �于 Q(\sqrt{4k^{2n} + 1}) 的理想�群的循�子群 [On the cyclic subgroups of ideal class group of Q(\sqrt{4k^{2n} + 1}) ], 数学学� 中文版 [Acta Math. Sinica] 第 42 � (1999) 第 6 期 : 1135–1139; sxxb-99-42(6)-1135.pdf (332 KB); [CAJ, PDF], cnki; 中国数学文摘 m2000055741 [html]; MR1756040 (2001e:11107) (reviewed by Z.-Y. Zheng) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1005.11055 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[102] M. R. Murty : Exponents of class groups of quadratic fields, Topics in Number theory (University Park, PA, 1997) (S. D. Ahlgren, G. E. Andrews and K. Ono, eds.), Math. Appl., vol. 467, Kluwer Acad. Publ., Dordrecht, 1999, pp. 229–239; MR1691322 (2000b:11123) (reviewed by K. Ono) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0993.11059 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[103] H. Taya : Iwasawa invariants and class numbers of quadratic fields for the prime 3, Proc. Amer. Math. Soc. 128 (2000), no. 5, 1285–1292; DOI: 10.1090/S0002-9939-99-05177-1 [PDF]; doi:10.2307/119633 [PDF (235 KB)], JSTOR; MR1641133 (2000j:11162) (reviewed by K. Horie) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0958.11069 (reviewed by F. Lemmermeyer) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[104] Y. Kishi and K. Miyake : Parametrization of the quadratic fields whose class numbers are divisible by three, J. Number Theory 80 (2000), no. 2, 209–217; doi:10.1006/jnth.1999.2455 [PDF (135 K)]; MR1740511 (2000m:11106) (reviewed by F. Lemmermeyer) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0976.11050 (reviewed by F. Lemmermeyer) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[105] K. Soundararajan : Divisibility of class numbers of imaginary quadratic fields, J. London Math. Soc. (2) 61 (2000), Part 3, 681–690; doi: 10.1112/S0024610700008887

[S0024610700008887a.pdf (291 Kb), CJO; 681.full.pdf,

Oxford Journals]; 57133971.pdf (287 KB), Academic Search Complete, EBSCO; MR1766097 (2001i:11128) (reviewed by M. R. Murty) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1018.11054 (reviewed by K. Yamamura) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[106] Z. Cao and X. Dong : Diophantine equations and class number of imaginary quadratic fields, Discuss. Math. Gen. Algebra Appl. 20 (2) (2000) 199–206; [PDF, PS]; MR1815104 (2001k:11222) (reviewed by B. Sodaigui) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0979.11020 (reviewed by I. Gaál) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[107] 董 �蕾, 曹珍富 [Dong, X.-L., Cao, Z.-F.] : 一�虚二次域� 数的可除性和一�著名�果�一的新�明 [A new and brief proof of the divisibility result of class number of a kind of imaginary quadratic fields ], ��江大学自然科学学� [Heilongjiang Daxue Ziran Kexue Xuebao; J. Nat. Sci. Heilongjiang Univ.] 第 18 � (2001) 第 1 期 : 8–11, 16; [CAJ, PDF], cnki; 中国数学文摘 m2002010140 [html]; MR1839270; Zbl 1076.11514.

[108] T. Komatsu : A family of infinite pairs of quadratic fields ℚ(\sqrt{D}) and ℚ(\sqrt{−D}) whose class numbers are both divisible by 3, Acta Arith. XCVI (2001), fasc. 3, 213– 221; doi:10.4064/aa96-3-2 [pdf_aa96-3-02.pdf (129.28 Kb)]; MR1814277 (2001m:11195) (reviewed by A. Srinivasan) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0987.11067 (reviewed by Zhang X.) [html, DVI, ps, PDF, TeX].

[109] D. Byeon : Indivisibility of class numbers and Iwasawa λ-invariants of real quadratic fields, Compositio. Math. 126 (2001), no. 3, 249–256; doi:10.1023/A:1017561005538

                                                            [t2116565763k01g4.pdf  (86.2  KB),  Springer;
                                                            S0010437X01000331a.pdf (86 KB), CJO]; MR1834738

(2002c:11148) (reviewed by T. Metsänkylä) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1014.11068 (reviewed by H. Taya) [html, PDF, XML, ASCII, DVI, PS, BibTeX]; Erratum : z11-erratum.pdf, available at http://www. math.snu.ac.kr/˜ dhbyeon/publication.htm.

[110] D. Byeon : Divisibility properties of class numbers, Trends in Math. 4 (2001), No. 1, 26–30; 100250.dvi, 100250.pdf.

[111] 小松亨 : An infinite family of pairs of quadratic fields ℚ(\sqrt{D}) and ℚ(\sqrt{−D}) whose class numbers are both divisible by 3, [Proceedings of the Workshop on Number Theory 2001] (K. Komatsu and K. Hashimoto, eds.), 早稲田大学, 2001, pp. 141–150.

[112] G. Yu : A note on the divisibility of class numbers of real quadratic fields, J. Number Theory 97 (2002), no. 1, 35– 44; doi: 10.1006/jnth.2001.2773 [PDF (118 K)]; MR1939135 (2003m:11187) (reviewed by M. R. Murty) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1036.11057 (reviewed by K. Yamamura) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[113] D. Byeon : A note on the existence of certain infinite families of imaginary qudaratic fields, J. Number Theory 97 (2002), no. 1, 165–170; doi:10.1006/jnth.2002.2787 [PDF (92 K)]; MR1939143 (2003i:11156) (reviewed by V. Vatsal) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1036.11050 (reviewed by R. A. Mollin) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[114] � 茂� [Le, M.-H.] : 虚二次域 Q(\sqrt{a^{2} − 4k^{n}})�数的可除性 [The divisibility of the class numbers of imaginary quadratic fields Q(\sqrt{a^{2} − 4k^{n}}) ], 吉首大学学� （自然科学版） [Jishou Daxue Xuebao; J. Jishou Univ. Nat. Sci. Ed.] 第 23 � (2002) 第 4 期 : 1–3; [CAJ, PDF], cnki; 中国数学文摘 m2003055269 [html]; MR1950368.

[115] T. Komatsu : An infinite family of pairs of quadratic fields ℚ(\sqrt{D}) and ℚ(\sqrt{mD}) whose class numbers are both divisible by 3, Acta Arith. 104 (2002), fasc. 2, 129–136; doi:10.4064/aa104-2-3 [pdf_aa104-2-03.pdf (134.28 Kb)]; MR1914248 (2003f:11166) (reviewed by A. Srivasan) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1004.11062 (reviewed by E. Nart Vinals) [html, PDF, XML, ASCII, DVI, PS, Bib-TeX].

[116] K. Chakraborty and M. R. Murty : On the number of real quadratic fields with class number divisible by 3, Proc. Amer. Math. Soc. 131 (2003), no. 1, 41–44; DOI: 10.1090/S0002-9939-02-06603-0 [PDF]; doi:10.2307/1194222 [PDF (134 KB)], JSTOR; MR1929021 (2003m:11184) (reviewed by X. Zhang) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1024.11073 (reviewed by H. Yokoi) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[117] D. Byeon and E. Koh : Real quadratic fields with class number divisible by 3, Manuscripta Math. 111 (2003), fasc. 2, 261–263; DOI: 10.1007/s00229-003-0379-z [wmm6jv8d0ar59yy5.pdf (87.6 KB)]; MR1989426 (2004d:11105) (reviewed by X. Zhang) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1125.11060 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[118] D. Byeon : Existence of certain fundamental discriminants and class numbers of real quadratic fields, J. Number Theory 98 (2003), no. 2, 432–437; doi:10.1016/S0022-314X(02)00050-1 [PDF (110 K)]; MR1955426 (2003k:11169) (reviewed by T. Metsänkylä) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1036.11055 (reviewed by R. A. Mollin) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[119] F. Luca : A note on the divisibility of class numbers of real quadratic fields, C. R. Math. Acad. Sci. Soc. R. Can. 25 (2003), no. 3, 71–75; MR1999181 (2004g:11099) (reviewed by R. B. Osburn) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1100.11038 (reviewed by R. A. Mollin) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[120] I. Kimura : A note on the existence of certain infinite families of imaginary quadratic fields, Acta Arith. 110 (2003), fasc. 1, 37–43; doi:10.4064/aa110-1-3 [pdf_aa110-1-03.pdf (116.27 Kb)]; MR2007542 (2004i:11129) (reviewed by J. O. D. Lopes) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1062.11070 (reviewed by K. Yamamura) [html, PDF, XML, ASCII, DVI, PS, BibTeX]; Correction : ibid. 114 (2004), no. 4, 397; doi:10.4064/aa114-4-8 [pdf_aa114-4-08.pdf (47.42 Kb)]; MR2102466.

[121] H. Ichimura : Note on the class numbers of certain real quadratic fields, Abh. Math. Sem. Univ. Hamburg 73 (2003), 281–288; DOI: 10.1007/BF02941283 [b8867u5k75l3w953.pdf (260.1 KB)]; MR2028521 (2004k:11174) (reviewed by F. Diaz y Diaz) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1050.11090 (reviewed by L. Skula) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[122] � 茂� [Le, M.-H.] : 虚二次域�数的可除性 [Divisibility of class numbers of imaginary quadratic fields ], 湛江�范学院学 � [J. Zhanjiang Teachers College] 第 24 � (2003) 第 3 期 : 1–3; [CAJ, PDF], cnki; 中国数学文摘 m2004033100 [html].

[123] Le, M.-H. [� 茂�], Chen, X.-G. [� �庚] : The divisibility of class numbers of imaginary quadratic fields [虚二次域�数的可除性], 黄��范学院学� [Huanggang Shifan Xueyuan Xuebao; J. Huanggang Normal Univ.] 第 23 � (2003) 第 6 期 : 1–3, 7; [CAJ, PDF], cnki; 中国数学文摘 m2004055989 [html].

[124] D. Byeon : Class numbers of quadratic fields ℚ(\sqrt{D}) and ℚ(\sqrt{tD}), Proc. Amer. Math. Soc. 132 (2004), no. 11, 3137–3140; DOI: 10.1090/S0002-9939-04-07536-7 [PDF]; doi:10.2307/4097403 [PDF (155 KB)], JSTOR; MR2073286 (2005c:11135) (summary) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 1061.11054 (reviewed by F. Lemmermeyer) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[125] K. Belabas : On quadratic fields with large 3-rank, Math. Comp. 73 (2004), no. 248, 2061–2074; DOI: 10.1090/S0025-5718-04-01632-1 [PDF]; doi:10.2307/4100069 [PDF (413 KB)], JSTOR; MR2059751 (2005c:11132) (reviewed by M. Olivier) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1051.11055 (reviewed by V. Ennola) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[126] M. Delong : Using elliptic curves to produce quadratic number fields of high three-rank, Rocky Mountain J. Math. 34 (2004), No. 2, 599–618; doi:10.1216/rmjm/1181069870, euclid.rmjm/1181069870 [PDF (99 KB)]; MR2072797 (2005e:11135) (reviewed by A. Bremner) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1107.11045 (reviewed by V. Ennola) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[127] R. A. Mollin : Class numbers, quadratics, and exponential Diophantine equations, JP J. Algebra Number Theory Appl. 4 (2004), no. 3, 537–548; MR2142479 (2005m:11202) (reviewed by Y. Bugeaud) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 1088.11079 (reviewed by A. S. Togbe) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[128] 曹珍富 [Cao, Z.-F.] : 虚二次域�数的可除性 [The divisibility of the class number of imaginary quadratic fields ], 数学年刊 A� (中文版) [Chinese Ann. Math. Ser. A] 第 25 � (2004) 第 3 期 : 397–406; [CAJ, PDF], cnki; 中国数学文摘 m2005033112 [html]; MR2081181 (2005e:11144) (reviewed by M.-H. Le) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1062.11069 (reviewed by Le, M.) [html, PDF, XML, ASCII, DVI, PS, Bib-TeX].

[129] Yang, D. (� �) and Zhang, X. (� �科) : Quadratic number fields with class numbers divisible by a prime q, Thinghua Sci. Technol. [清�大学学� (英文版)] 9 (2004), no. 4, 475–481; test019.pdf; [CAJ, PDF], cnki; MR2090126 (2005g:11209) (reviewed by C. J. Parry) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 1082.11072 (reviewed by K. Yamamura) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[130] 中野伸 : 代数体の類数の可除性について, 第 3 回北陸数論研究集会報告集 [Proceedings of the 3rd Workshop on Number Theory] (金沢大学サテライトプラザ, 2004) (平林幹人, 野村明人, 木村巌, 菅野孝史編), 2005, pp. 50–59.

[131] 田谷久雄 : 代数体の類数の可除性非可除性について, 第 3 回北陸数論研究集会報告集 [Proceedings of the 3rd Workshop on Number Theory] (金沢大学サテライトプラザ, 2004) (平林幹人, 野村明人, 木村巌, 菅野孝史編), 2005, pp. 61–83.

[132] 山村健 : 2 次 (拡大) 体の類数の可除性および非可除性に関する文献 (2-part のみに関するものは除く), 第 3 回北陸数論研究集会報告集 [Proceedings of the 3rd Workshop on Number Theory] (金沢大学サテライトプラザ, 2004) (平林幹人, 野村明人, 木村巌, 菅野孝史編), 2005, pp. 124–138.

[133] D. Byeon : Imaginary quadratic fileds with noncyclic ideal class group, Ramanujan J. 11 (2006), no. 2, 159–163; DOI: 10.1007/s11139-006-6504-3 [a150718621134044.pdf (157.0 KB)]; MR2267671 (2007j:11147) (reviewed by T. P. N. Neto) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1161.11391 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[134] D. Byeon : Real quadratic fields with class number divisible by 5 or 7, Manuscripta Math. 120 (2006), fasc. 2, 211–215; DOI: 10.1007/s00229-006-0002-1 [a2v72176rl576022.pdf (90.6 KB)]; MR2234249 (2007f:11124) (reviewed by X. Zhang) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1153.11337 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[135] P. Jenkins and K. Ono : Divisibility criteria for class numbers of imaginary quadratic fields, Acta Arith. 125 (2006), fasc. 3, 285–289; doi:10.4064/aa125-3-5 [pdf_aa125-3-05.pdf (90.61 Kb)]; MR2276195 (2007i:11148) (reviewed by A. Nomura) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1153.11055 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[136] K. Chakraborty : Divisibility of class numbers of real quadratic fields, 解析的整数論とその周辺 [Analytic Number Theory and Surrounding Areas] (京都大学数理解析研究所, 2004) (天羽雅昭編), 数理解析研究所講究録 [RIMS Kokyuroku] 1511, 2006, 188–196; 1511-23.pdf; 1511-23.pdf (804.41 kB), URI: http://hdl.handle.net/2433/58595.

[137] C. Erickson, N. Kaplan, N. Mendoza, A. M. Pacelli and T. Shayler : Parametrized families of quadratic number fields with 3-rank at least 2, Acta Arith. 130 (2007), fasc. 2, 141–147; doi:10.4064/aa130-2-3 [pdf_aa130-2-03.pdf (105.49 Kb)]; MR2357651 (2009a:11223) (reviewed by R. B. Osburn); [html, PDF, DVI, PostScript, BibTeX]; Zbl 1147.11063 (reviewed by F. Luca) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[138] D. R. Heath-Brown : Quadratic class numbers divisible by 3, Funct. Approx. Comment. Math. 37 (2007), part 1, 203–211; euclid.facm/1229618751 [PDF]; MR2357319 (2008j:11161) (reviewed by J. Ritter); [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 1140.11050 (reviewed by W. Narkiewicz) [html, PDF, XML, ASCII, DVI, PS, BibTeX]; Corrigendum : arXiv:1009.4630 [PDF, PS, DVI, TeX].

[139] R. A. Mollin : Class numbers of quadratic fields, Mersenne numbers, Fermat numbers, and exponential Diophantine equations, JP J. Algebra Number Theory Appl. 9 (2007), no. 1, 129–133; [online]; MR2407811 (2009f:11140) (reviewed by L. Washington) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1207.11108 (reviewed by A. S. Togbe) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[140] R. A. Mollin : Class numbers of real quadratic orders, generalized Fermat numbers, and exponential Diophantine equations, Far East J. Math. Sci. (FJMS) 27 (2007), no. 1, 71– 80; [online]; MR2402544 (2009a:11237) (reviewed by A. Srinivasan) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1204.11177 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[141] 佐藤篤 : 類数が 5 で割り切れる二次体について, 仙台数論及び組合せ論小研究集会 2006 (第 3 回) 報告集 (東北大学, 2007) (宗政昭弘, 田谷久雄編), 2007, pp. 17–26; sato.pdf, sato.dvi.

[142] 堀博之 : 2 次体の類数が 3 で割り切れるための条件について, 早稲田大学整数論研究集会 2007 報告集 [Proceedings of the workshop on Number Theory 2007] (早稲田大学, 2007) (橋本喜一朗, 小松啓一編), 早稲田大学数学応用数学研究所, 2007, pp. 94–108.

[143] F. Luca and A. M. Pacelli : Class groups of quadratic fields of 3-rank at least 2: Effective bounds, J. Number Theory 128 (2008), no. 4, 796–804; doi:10.1016/j.jnt.2007.05.014 [PDF (121 K)]; MR2400040 (2008m:11217) (reviewed by R. B. Osburn) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1167.11038 (reviewed by R. A. Mollin) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[144] A. Pekin : On imaginary quadratic fields whose class numbers are divisible by 3, Int. J. Contemp. Math. Sci. 3 (2008), no. 7, 327–329; pekinIJCMS5-8-2008.pdf; MR2400098 (2009b:11187) (reviewed by M. G. Leu) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1142.11364 (from the text) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[145] Y. Kishi : A new family of imaginary quadratic fields whose class number is divisible by five, J. Number Theory 128 (2008), no. 8, 2450–2458; doi:10.1016/j.jnt.2008.02.016 [PDF (126 K)]; MR2394830 (2009c:11173) (reviewed by S. Louboutin) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1173.11056 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[146] K. Chakraborty, F. Luca, and A. Mukhopadhyay : Class numbers with many prime factors, J. Number Theory 128 (2008), no. 9, 2559–2558; doi:10.1016/j.jnt.2008.03.010 [PDF (161 K)]; MR2444211 (2010a:11214) (reviewed by R. B. Osburn) [html, PDF, DVI, PostScript, BibTeX]; Zbl pre05368230 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[147] A. Pekin : Indivisibility of class numbers of real quadratic fields, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 24 (2008), No. 3, 267–270; [amapn24_326.ps.gz (112 kilobytes), amapn24_326.pdf (140 kilobytes)]; MR2469947 (2009m:11189) (summary) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 1164.11070 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[148] K. Chakraborty, F. Luca, and A. Mukhopadhyay : Exponents of class groups of real quadratic fields, Int. J. Number Theory 4 (2008), No. 4, 597–611; DOI: 10.1142/S1793042108001559 [PDF (248 KB)]; 33911235.pdf (238 KB), Academic Search Complete, EBSCO; MR2441794 (2009i:11131) (reviewed by S. W. Zhang) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1165.11081 (reviewed by F. Lemmermeyer) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[149] D. Byeon and S. Lee : Divisibility of class numbers of imaginary quadratic fields whose discriminant has only two prime factors, Proc. Japan Acad. Ser. A Math. Sci. [日本学士院紀要] 84 (2008), No. 1, 8–10; doi:10.3792/pjaa.84.8, euclid.pja/1201186678 [PDF (65 KB)]; MR2381177 (2008k:11113) (summary) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1226.11117 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[150] Y. Kishi : Note on the divisibility of the class number of certain imaginary quadratic fields, Glasg. Math. J. 51 (2009), Part 1, 187–191; doi:10.1017/S001708950800462X [PDF (67 KB)]; MR2471686 (2009m:11186) (reviewed by K. Chakraborty) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1211.11124 (reviewed by R. A. Mollin) [html, PDF, XML, ASCII, DVI, PS, BibTeX]; Corrigendum : ibid. 52 (2010), Part 1, 207–208; doi:10.1017/S0017089509990371 [PDF (37 KB)]; MR2587831 (2011a:11199) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1211.11125 [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[151] Y. Kishi : On D_{5}-polynomials with integer coefficients, Annal. Math. Blaise Pascal 16 (2009), no. 1, 113–125; doi: 10.5802/ambp.258 [AMBP_2009__16_1_

                                                            113_0.pdf]; AMBP_2009__16_1_113_0.djvu, AMBP_2009__

16_1_113_0.pdf, Numdam; MR2514531 (2010f:11160) (reviewed by H. Oukhaba) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 1173.11059 (reviewed by D. Byeon) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[152] D. Byeon : Quadratic fields with noncyclic 5- or 7class groups, Ramanujan J. 19 (2009), no. 1, 71–77; DOI: 10.1007/s11139-008-9129-x [c21r55qx5627kx61.pdf (246.4 KB)]; MR2501238 (2010h:11177) (reviewed by F. Sairaiji) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1195.11143 (reviewed by F. Nicolae) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[153] S. R. Louboutin : On the divisibility of the class number of imaginary quadratic number fields, Proc. Amer. Math. Soc. 137 (2009), no. 12, 4025–4028; DOI: 10.1090/S0002-9939-09-10021-7 [PDF]; MR2538563 (2010g:11189) (reviewed by T. Metsänkylä) [html, PDF, DVI, PostScript, BibTeX]; Zbl pre05638160 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[154] Y. Kishi : On the ideal class group of certain quadratic fields, Glasg. Math. J. 52 (2010), Part 3, 575– 581; DOI: 10.1017/S0017089510000431 [PDF]; MR2679915 (2011f:11146) (reviewed by K. Chakraborty) [html, PDF, DVI, PostScript, BibTeX]; Zbl pre05799544 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[155] 伊東杏希子 [A. Ito] : On the divisibility of class numbers of imaginary quadratic fields ℚ(\sqrt{3^{2e} − 4q^{n}}) and some Diophantine equations, 解析数論およびその周辺の諸問題 [Analytic number theory and related topics] (津村博文, 小森靖編), 数理解析研究所講究録 [RIMS Kokyuroku] 1710 (2010), 101–112.

[156] 岸康弘 : 3-rank が 2 以上のイデアル類群を持つ虚 2 次体の族, 第 8 回北陸数論研究集会報告集 ( 「ガロア理論とその周辺」とのジョイント開催) [Proceedings of the 8th Workshop on Number Theory] (金沢大学サテライトプラザ, 2009) (平林幹人, 野村明人, 山下浩, 木村巌, 菅野孝史編), 2010, pp. 71–80.

[157] A. Ito : Remarks on the divisibility of class numbers of imaginary quadratic fields ℚ(\sqrt{2^{k} − q^{n}}), Glas. Math. J. 53 (2011), Part 2, 379–389; DOI: 10.1017/S0017089511000012 [PDF]; MR2783167 (2012d:11211) (reviewed by K. Chakraborty) [html, PDF, DVI, PostScript, BibTeX].

[158] P. J. Cho : Sum of three squares and class numbers of imaginary quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), No. 6, 91–94; doi:10.3792/pjaa.87.91, euclid.pja/1306934064 [PDF (84 KB)]; MR2803887 (reviewed by W. Narkiewicz) [html, PDF, DVI, PostScript, BibTeX].

[159] K. Ishii : On the divisibility of the class number of imaginary quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), No. 8, 142–143; doi:10.3792/pjaa.87.142, euclid.pja/1317647396 [PDF (51 KB)].

[160] A. Ito : A note on the divisibility of class numbers of imaginary quadratic fields Q(\sqrt{a^{2} − k^{n}}), Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), No. 9, 151–155; doi:10.3792/pjaa.87.151, euclid.pja/1320417392 [PDF (101 KB)].

[161] 伊東杏希子 : ある二次体の類数の 3-divisibility について, 第５回福岡数論研究集会報告集 (九州大学, 2010) (金子昌信, 権寧魯, 岸康弘編), 2011, pp. 33–43; 004-Ito.pdf.

[162] Zhu, M. and Wang, T. : The divisibility of the class number of the imaginary quadratic field Q(\sqrt{2^{2m} − k^{n}}), Glas. Math. J. 54 (2012), Part 1, 149–154; DOI: 10.1017/S0017089511000486 [PDF (67 KB)].