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Hecke’s integral formula for relative quadratic extensions of algebraic number fields. (English) Zbl 1138.11052

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

MSC:

11R42 Zeta functions and \(L\)-functions of number fields
11R11 Quadratic extensions
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References:

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