### 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 |
---|---|

Pages (from-to) | 139-154 |

Number of pages | 16 |

Journal | Nagoya Mathematical Journal |

Volume | 189 |

Publication status | Published - 2008 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Nagoya Mathematical Journal*,

*189*, 139-154.

**Hecke's integral formula for relative quadratic extensions of algebraic number fields.** / Yamamoto, Shuji.

Research output: Contribution to journal › Article

*Nagoya Mathematical Journal*, vol. 189, pp. 139-154.

}

TY - JOUR

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

AU - Yamamoto, Shuji

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.

UR - http://www.scopus.com/inward/record.url?scp=39749111009&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39749111009&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:39749111009

VL - 189

SP - 139

EP - 154

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

ER -