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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