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Hecke’s Integral Formula for Relative Quadratic Extensions of Algebraic Number Fields

Published online by Cambridge University Press:  11 January 2016

Shuji Yamamoto
Shuji Yamamoto*
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan
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Abstract

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Let K/F be a quadratic extension of number fields. After developing a theory of the Eisenstein series over F, we prove a formula which expresses a partial zeta function of K as a certain integral of the Eisenstein series. As an application, we obtain a limit formula of Kronecker’s type which relates the 0-th Laurent coefficients at s = 1 of zeta functions of K and F.

Keywords

11R4211R11
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 189 , 2008 , pp. 139 - 154
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

References

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