TY - JOUR

T1 - Hecke's integral formula for relative quadratic extensions of algebraic number fields

AU - Yamamoto, Shuji

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2008

Y1 - 2008

N2 - 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 if 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.

AB - 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 if 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.

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U2 - 10.1017/S0027763000009521

DO - 10.1017/S0027763000009521

M3 - Article

AN - SCOPUS:39749111009

VL - 189

SP - 139

EP - 154

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

ER -