### 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 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.

Original language | English |
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Pages (from-to) | 139-154 |

Number of pages | 16 |

Journal | Nagoya Mathematical Journal |

Volume | 189 |

DOIs | |

Publication status | Published - 2008 Jan 1 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Yamamoto, S. (2008). Hecke's integral formula for relative quadratic extensions of algebraic number fields.

*Nagoya Mathematical Journal*,*189*, 139-154. https://doi.org/10.1017/S0027763000009521