代数体の類数の可除性および非可除性に関する文献 (2 次 (拡大) 体のみに関するものおよび

bad part のみに関するものは除く) (2012 年 2 月更新版)

[1] 市川洋 : 與えられた有限 Abel 群を Idealklassengruppe の部分群にもつ代數體の構成, 數學第 3 卷 (1951), 第 1 號, 48–49; 3_48.pdf (315 K), Journal@rchive, JST.

[2] H. Cohn : A device for generating fields of even class number, Proc. Amer. Math. Soc. 7 (1956), no. 4, 595–598; DOI: 10.1090/S0002-9939-1956-0079613-9 [PDF]; doi:10.2307/2033356 [PDF (142 KB)], JSTOR; MR0079613 (18, 114b) (reviewed by H. Davenport) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0071.03402 (reviewed by Z. Suetuna) [scanned image].

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[7] O. Yahagi : Construction of number fields with prescribed l-class groups, Tokyo J. Math. 1 (1978), No. 2, 275–283; doi:10.3836/tjm/1270216499, euclid.tjm/1270216499 [PDF (938 KB)]; MR0519197 (80d:12004) (reviewed by R. Massy; reprinted in Reviews in Number Theory, volume 5A, R26-259) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0403.12011 (reviewed by R. Mollin) [scanned image].

[8] J. Sonn : Class groups and Brauer groups, Israel J. Math. 34 (1979), Nos. 1-2, 97–105; DOI: 10.1007/BF02761826 [v5627083q27605q4.pdf (348.0 KB)]; MR0571397 (81g:12012) (reviewed by B. Fein; reprinted in Reviews in Number Theory, volume 5A, R54-215L) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0433.12005 (abstract) [scanned image].

[9] S. Kobayashi : Divisibility of class numbers of real cyclic extensions of degree 4 over ℚ, J. Reine Angew. Math. 307/308 (1979), 365–372; doi: 10.1515/crll.1979.307-308.365 [PDF

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[10] G. Cornell : Abhyankar’s lemma and the class group, Number theory, Carbondale 1979 (Proc. Southern Illinois Conf., Southern Illinois Univ., Carbondale, Ill., 1979) (M. B. Nathanson, eds.), Lecture Notes in Math., vol. 751, Springer-Verlag, New York and Berlin, 1979, pp. 82–88; DOI: 10.1007/BFb0062697 [56m58j8163696p10.pdf (212.7 KB)]; MR0564924 (82c:12007) (reviewed by S. Khanduja; reprinted in Reviews in Number Theory, volume 5A, R26-273) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0423.12009 (reviewed by P. Draxl) [scanned image].

[11] S. Kobayashi : Divisibilité du nombre de classes des corps abéliens réels, J. Reine Angew. Math. 320 (1980), 142–149; doi: 10.1515/crll.1980.320.142 [PDF (929 KB)];

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[12] K. Iimura : On the l-class group of an algebraic number field, J. Reine Angew. Math. 322 (1981), 136– 144; DOI: 10.1515/crll.1981.322.136 [PDF (1196 KB)];

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[13] 市村文男 [Ichimura, H.] : 3, 4, 5 次体に於る類数の可除性の問題, Z_{p} 拡大およびその関連理論の研究 [Studies on the Z_{P} Extension and Its Neighboring Theory] (京都大学数理解析研究所, 1981) (藤崎源二郎編), 数理解析研究所講究録 [RIMS Kokyuroku] 440, 1981, 179–190; 0440-18.pdf; 0440-18.pdf (602.07 kB), URI: http://hdl.handle.net/2433/102806.

[14] H. Ichimura : On 2-rank of the ideal class groups of totally real number fields, Proc. Japan Acad. Ser. A Math. Sci. [日本学士院紀要] 58 (1982), No. 7, 329–332; doi:10.3792/pjaa.58.329, euclid.pja/1195515930 [PDF (368 KB)]; MR0682696 (84h:12025) (reviewed by Y. Furuta; reprinted in Reviews in Number Theory, volume 5B, R80-601) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0514.12015 (reviewed by T. Takeuchi) [scanned image].

[15] J. Sonn : Direct summands of class groups, J. Number Theory 17 (1983), no. 3, 343–349; doi:10.1016/0022-314X(83)90052-5 [PDF (341 K)]; MR0724533 (85e:11091) (reviewed by R. Massey; reprinted in Reviews in Number Theory, volume 5B, R32-618) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0519.12008 (reviewed by R. Mollin) [scanned image]

[16] S. Nakano : On the construction of certain number fields, Tokyo J. Math. 6 (1983), No. 2, 389–395; doi:10.3836/tjm/1270213878, euclid.tjm/1270213878 [PDF (659 KB)]; MR0732091 (85a:11023) (reviewed by P. Damey; reprinted in Reviews in Number Theory, volume 5B, R29-625) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0529.12005.

[17] H. Yokoi : On the Diophantine equation x^{2} − py^{2} = ±4q and the class number of real subfields of a cyclotomic field, Nagoya Math. J. 91 (1983), 151–161; euclid.nmj/1118787268 [PDF (884 KB)]; MR0716789 (85b:11098) (reviewed by T. Metsänkylä; reprinted in Reviews in Number Theory, volume 5B, R29-630) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0506.10012 (Autorreferat) [scanned image].

[18] F. Gerth III : Asymptotic results for class number divisibility in cyclotomic fields, Canad. Math. Bull. 26 (1983), no. 4, 464–472; DOI: 10.4153/CMB-1983-075-

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[19] S. Nakano : Class numbers of pure cubic fields, Proc. Japan Acad. Ser. A Math. Sci. [日本学士院紀要] 59 (1983), no. 6, 263–265; doi:10.3792/pjaa.59.263, euclid.pja/1195515524 [PDF (238 KB)]; MR0718617 (84j:12005) (reviewed by P. Damey; reprinted in Reviews in Number Theory, volume 5B, R16-606) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0515.12002 (reviewed by H. Yokoi) [scanned image].

[20] M. Watabe : On certain cubic fields. IV, Proc. Japan Acad. Ser. A Math. Sci. [日本学士院紀要] 59 (1983), No. 8, 387–389; doi:10.3792/pjaa.59.387, euclid.pja/1195515411 [PDF (285 KB)]; MR0726531 (85b:11087) (reviewed by H. Bruenotte; reprinted in Reviews in Number Theory, volume 5B, R16-610) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0542.12002 (reviewed by M.-N. Gras) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[21] 市村文男, 小豆畑隆 : 代数体の類数の可除性について, 整数論研究集会報告集 (九州大学, 1982) (白谷克己編), 1983, pp. 75–88.

[22] T. Azuhata and H. Ichimura : On the divisibility problem of the class numbers of algebraic number fields, J. Fac. Sci. Univ. Tokyo, Sect. I A Math. [東京大学理学部紀要第 I 類 A 数学] 30 (1984), No. 3, 579–585; jfs300307.pdf (253 Kb), URI: http://hdl.handle.net/2261/6387; MR0731519 (85a:11021) (reviewed by P. Damey; reprinted in Reviews in Number Theory, volume 5B, R29-623) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 0532.12006 (reviewed by F. Halter-Koch) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[23] S. Nakano : On the 2-rank of ideal class groups of pure number fields, Arch. Math. (Basel) 42 (1984), No. 1, 53–57; DOI: 10.1007/BF01198128 [kn2g5u1722314160.pdf (216.7 KB)]; MR0751471 (85j:11146) (reviewed by L. N. Childs; reprinted in Reviews in Number Theory, volume 5B, R29-644) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0531.12006 (reviewed by H. Yokoi) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[24] A. Endô : Remark on the divisibility of the class numbers of certain quartic numbers fields by 5, Proc. Amer. Math. Soc. 91 (1984), no. 4, 513–517; DOI: 10.1090/S0002-9939-1984-0746079-X [PDF]; doi:10.2307/2044790 [PDF (157 KB)], JS-TOR; MR0746079 (86c:11093) (reviewed by C. J. Parry; reprinted in Reviews in Number Theory, volume 5B, R29-657) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0522.12007 (Autorreferat) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

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[33] 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)];

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[43] S. Jakubec : On divisibility of h^{+} by the prime 3, Rocky Mountain J. Math. 24 (1994), no. 4, 1467–1479; doi:10.1216/rmjm/1181072349, euclid.rmjm/1181072349 [PDF (182 KB)]; MR1322239 (95m:11119) (reviewed by T.

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