On the Stark–Shintani units and the ideal class groups in the cyclotomic Zp-extensions of class fields over real quadratic fields

Acta Arithmetica ◽

10.4064/aa102-1-2 ◽

2002 ◽

Vol 102 (1) ◽

pp. 21-26 ◽

Cited By ~ 1

Author(s):

Tsuyoshi Itoh

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Real Quadratic Fields ◽

Ideal Class Groups ◽

Class Fields ◽

Real Quadratic ◽

The Ideal

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Tables of ideal class groups of real quadratic fields

Proceedings of the Japan Academy Series A Mathematical Sciences ◽

10.3792/pjaa.64.347 ◽

1988 ◽

Vol 64 (9) ◽

pp. 347-349 ◽

Cited By ~ 5

Author(s):

Michiyo Saito ◽

Hideo Wada

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Real Quadratic Fields ◽

Ideal Class Groups ◽

Real Quadratic

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Ideal class groups and their subgroups of real quadratic fields

Science in China Series A Mathematics ◽

10.1007/bf02878670 ◽

1997 ◽

Vol 40 (9) ◽

pp. 909-916 ◽

Cited By ~ 1

Author(s):

Lawrence C. Washington ◽

Xianke Zhang

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Real Quadratic Fields ◽

Ideal Class Groups ◽

Real Quadratic

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Modification of Cohen-Lenstra heuristics for ideal class groups and numbers of certain real quadratic fields

Chinese Science Bulletin ◽

10.1007/bf02883192 ◽

1997 ◽

Vol 42 (23) ◽

pp. 1959-1962

Author(s):

L. C. Washington ◽

Zhang Xianke

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Real Quadratic Fields ◽

Ideal Class Groups ◽

Real Quadratic

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On the exponent of the ideal class groups of complex quadratic fields.

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1972-0289454-4 ◽

1972 ◽

Vol 31 (2) ◽

pp. 433-433

Author(s):

David W. Boyd ◽

H. Kisilevsky

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Ideal Class Groups ◽

The Ideal

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On the ideal class groups of the $p$-class fields of quadratic number fields

Proceedings of the Japan Academy Series A Mathematical Sciences ◽

10.3792/pjaa.68.62 ◽

1992 ◽

Vol 68 (3) ◽

pp. 62-67 ◽

Cited By ~ 1

Author(s):

Katsuya Miyake

Keyword(s):

Number Fields ◽

Ideal Class ◽

Quadratic Number ◽

Class Groups ◽

Ideal Class Groups ◽

Quadratic Number Fields ◽

Class Fields ◽

The Ideal

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The selmer groups of elliptic curves and the ideal class groups of quadratic fields

Communications in Algebra ◽

10.1080/00927879708825980 ◽

1997 ◽

Vol 25 (7) ◽

pp. 2157-2167

Author(s):

Yen-Mei J. Chen

Keyword(s):

Elliptic Curves ◽

Quadratic Fields ◽

Selmer Groups ◽

Ideal Class ◽

Class Groups ◽

Ideal Class Groups ◽

The Ideal

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The ideal class groups of dihedral extensions over imaginary quadratic fields and the special values of the Artin L-function

Journal of Number Theory ◽

10.1016/j.jnt.2010.11.011 ◽

2011 ◽

Vol 131 (6) ◽

pp. 1062-1069

Author(s):

Yutaka Konomi

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Imaginary Quadratic Fields ◽

Special Values ◽

Ideal Class Groups ◽

Dihedral Extensions ◽

The Ideal

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On the Exponent of the Ideal Class Groups of Complex Quadratic Fields

Proceedings of the American Mathematical Society ◽

10.2307/2037547 ◽

1972 ◽

Vol 31 (2) ◽

pp. 433 ◽

Cited By ~ 3

Author(s):

David W. Boyd ◽

H. Kisilevsky

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Ideal Class Groups ◽

The Ideal

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A criterion for a certain type of imaginary quadratic fields to have $3$-ranks of the ideal class groups greater than one

Proceedings of the Japan Academy Series A Mathematical Sciences ◽

10.3792/pjaa.74.93 ◽

1998 ◽

Vol 74 (6) ◽

pp. 93-97 ◽

Cited By ~ 3

Author(s):

Yasuhiro Kishi

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Imaginary Quadratic Fields ◽

Ideal Class Groups ◽

The Ideal

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Units and Class Numbers of Real Quadratic Fields

Nagoya Mathematical Journal ◽

10.1017/s0027763000013295 ◽

1970 ◽

Vol 37 ◽

pp. 61-65

Author(s):

Hideo Yokoi

Keyword(s):

Quadratic Field ◽

Integral Solution ◽

Quadratic Fields ◽

Class Numbers ◽

Ideal Class ◽

Real Quadratic Field ◽

Pell’S Equation ◽

Real Quadratic Fields ◽

Real Quadratic ◽

The Ideal

The aim of this paper is to prove the following main theorem: THEOREM. For the discriminant d>0 of a real quadratic field let (x,y) = (t,u) be the least positive integral solution of Pell’s equation x2 — dy2 = 4 and put and denote by hd the ideal class number.

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