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2008 Hecke's integral formula for relative quadratic extensions of algebraic number fields
Shuji Yamamoto
Nagoya Math. J. 189: 139-154 (2008).

Abstract

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 $F$.

Citation

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Shuji Yamamoto. "Hecke's integral formula for relative quadratic extensions of algebraic number fields." Nagoya Math. J. 189 139 - 154, 2008.

Information

Published: 2008
First available in Project Euclid: 10 March 2008

zbMATH: 1138.11052
MathSciNet: MR2396585

Subjects:
Primary: 11R42
Secondary: 11R11

Rights: Copyright © 2008 Editorial Board, Nagoya Mathematical Journal

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Vol.189 • 2008
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