Class numbers of binary quadratic forms over algebraic number fields.

1979 ◽  
Vol 1979 (307-308) ◽  
pp. 353-364 ◽  
Keyword(s):  
Algebraic Number ◽  
Quadratic Forms ◽  
Number Fields ◽  
Class Numbers ◽  
Binary Quadratic Forms ◽  
Algebraic Number Fields

scholarly journals On S-class number relations of algebraic tori in Galois extensions of global fields

1991 ◽  
Vol 124 ◽  
pp. 133-144 ◽  
Author(s):  
Masanori Morishita
Keyword(s):  
Class Number ◽  
Quadratic Forms ◽  
Euler Number ◽  
Number Fields ◽  
Binary Quadratic Forms ◽  
Algebraic Number Fields ◽  
Algebraic Tori ◽  
Genus Theory ◽  
Class Number Formula ◽  
Number Formula

As an interpretation and a generalization of Gauss’ genus theory on binary quadratic forms in the language of arithmetic of algebraic tori, Ono [02] established an equality between a kind of “Euler number E(K/k)” for a finite Galois extension K/k of algebraic number fields and other arithmetical invariants associated to K/k. His proof depended on his Tamagawa number formula [01] and Shyr’s formula [Sh] which follows from the analytic class number formula of a torus. Later, two direct proofs were given by Katayama [K] and Sasaki [Sa].

A note on class numbers of algebraic number fields

2001 ◽  
pp. 372-373
Author(s):  
Ichiro Satake ◽  
Genjiro Fujisaki ◽  
Kazuya Kato ◽  
Masato Kurihara ◽  
Shoichi Nakajima
Keyword(s):  
Algebraic Number ◽  
Number Fields ◽  
Class Numbers ◽  
Algebraic Number Fields

A Note on the Class-Numbers of Algebraic Number Fields

1956 ◽  
Vol 78 (1) ◽  
pp. 51 ◽  
Author(s):  
N. C. Ankeny ◽  
R. Brauer ◽  
S. Chowla
Keyword(s):  
Algebraic Number ◽  
Number Fields ◽  
Class Numbers ◽  
Algebraic Number Fields
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