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Hecke's integral formula for quadratic extensions of a number field

Shuji Yamamoto
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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.

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Shuji Yamamoto. 2006-02-27. Hecke's integral formula for quadratic extensions of a number field. https://arxiv.org/abs/math/0602618

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