SPIEGELUNGSSATZ: A COMBINATORIAL PROOF FOR THE 4-RANK

International Journal of Number Theory ◽

10.1142/s1793042111005106 ◽

2011 ◽

Vol 07 (08) ◽

pp. 2157-2170

Author(s):

LAURENT HABSIEGER ◽

EMMANUEL ROYER

Keyword(s):

Quadratic Fields ◽

Combinatorial Proof ◽

System Of Equations ◽

Ideal Class ◽

Class Groups ◽

Ideal Class Groups ◽

The Spiegelungssatz is an inequality between the 4-ranks of the narrow ideal class groups of the quadratic fields [Formula: see text] and [Formula: see text]. We provide a combinatorial proof of this inequality. Our interpretation gives an affine system of equations that allows to describe precisely some equality cases.

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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 ◽

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Imaginary quadratic fields whose ideal class groups have 3-rank at least three

Journal of Number Theory ◽

10.1016/j.jnt.2016.06.019 ◽

2017 ◽

Vol 170 ◽

pp. 46-54

Author(s):

Yasuhiro Kishi ◽

Toru Komatsu

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Imaginary Quadratic Fields ◽

Ideal Class Groups

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A table of ideal class groups of imaginary quadratic fields

Proceedings of the Japan Academy ◽

10.3792/pja/1195520300 ◽

1970 ◽

Vol 46 (5) ◽

pp. 401-403 ◽

Author(s):

Hideo Wada

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Imaginary Quadratic Fields ◽

Ideal Class Groups

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On higher Fitting ideals of Iwasawa modules of ideal class groups over imaginary quadratic fields and Euler systems of elliptic units

Kyoto Journal of Mathematics ◽

10.1215/21562261-2366118 ◽

2013 ◽

Vol 53 (4) ◽

pp. 845-887 ◽

Author(s):

Tatsuya Ohshita

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Imaginary Quadratic Fields ◽

Euler Systems ◽

Ideal Class Groups ◽

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A Constructive Approach to Spiegelung Relations between 3-Ranks of Absolute Ideal Class Groups and Congruent Ones Modulo (3)2 in Quadratic Fields

Journal of Number Theory ◽

10.1006/jnth.1999.2498 ◽

2000 ◽

Vol 83 (1) ◽

pp. 1-49 ◽

Author(s):

Yasuhiro Kishi

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Constructive Approach ◽

Class Groups ◽

Ideal Class Groups

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Imaginary quadratic fields with noncyclic ideal class groups

The Ramanujan Journal ◽

10.1007/s11139-006-6504-3 ◽

2006 ◽

Vol 11 (2) ◽

pp. 159-163 ◽

Author(s):

Dongho Byeon

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Imaginary Quadratic Fields ◽

Ideal Class Groups

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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 ◽

Author(s):

Tsuyoshi Itoh

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Real Quadratic Fields ◽

Ideal Class Groups ◽

Class Fields ◽

Real Quadratic ◽

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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 ◽

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REMARKS ON QUADRATIC FIELDS WITH NONCYCLIC IDEAL CLASS GROUPS

Taiwanese Journal of Mathematics ◽

10.11650/tjm.19.2015.5081 ◽

2015 ◽

Vol 19 (5) ◽

pp. 1387-1399

Author(s):

Kwang-Seob Kim

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Ideal Class Groups

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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 ◽

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