Singular abelian surfaces and binary quadratic forms

Lecture Notes in Mathematics - Classification of Algebraic Varieties and Compact Complex Manifolds ◽

10.1007/bfb0066163 ◽

1974 ◽

pp. 259-287 ◽

Cited By ~ 17

Author(s):

Tetsuji Shioda ◽

Naoki Mitani

Keyword(s):

Quadratic Forms ◽

Binary Quadratic Forms ◽

Abelian Surfaces

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Class numbers of indefinite binary quadratic forms

Journal of Number Theory ◽

10.1016/0022-314x(82)90028-2 ◽

1982 ◽

Vol 15 (2) ◽

pp. 229-247 ◽

Cited By ~ 81

Author(s):

Peter Sarnak

Keyword(s):

Quadratic Forms ◽

Class Numbers ◽

Binary Quadratic Forms

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Sun's conjectures on fourth powers in the class group of binary quadratic forms

Journal of Number Theory ◽

10.1016/j.jnt.2009.06.009 ◽

2010 ◽

Vol 130 (1) ◽

pp. 192-197 ◽

Cited By ~ 1

Author(s):

Robert W. Fitzgerald

Keyword(s):

Quadratic Forms ◽

Class Group ◽

Binary Quadratic Forms

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

Nagoya Mathematical Journal ◽

10.1017/s0027763000003809 ◽

1991 ◽

Vol 124 ◽

pp. 133-144 ◽

Cited By ~ 5

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].

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