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

Published online by Cambridge University Press:  22 January 2016

Masanori Morishita
Masanori Morishita*
Affiliation:
Department of Mathematics, The Johns Hopkins University, Baltimore, MD 21218, U.S.A.
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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].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 124 , December 1991 , pp. 133 - 144
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

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