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

2000 ◽  
Vol 83 (1) ◽  
pp. 1-49 ◽  
Author(s):  
Yasuhiro Kishi
Keyword(s):  
Quadratic Fields ◽  
Ideal Class ◽  
Constructive Approach ◽  
Class Groups ◽  
Ideal Class Groups

scholarly journals SPIEGELUNGSSATZ: A COMBINATORIAL PROOF FOR THE 4-RANK

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 ◽  
Affine System

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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