Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Hohto Bekki
Affiliation:

MPIM
Date:

Wed, 2018-03-07 14:30 - 15:30 The classical Hecke's integral formula expresses the partial zeta function of real quadratic fields as an integral of the real analytic Eisenstein series along a certain closed geodesic on the modular curve. In this talk, we present a generalization of this formula in the case of an arbitrary extension E/F of number fields. As an application, we present the residue formula and Kronecker's limit formula for an extension E/F of number fields, which gives an integral expression of the residue and the constant term at s=1 of the "relative'' partial zeta function associated to E/F. This gives a simultaneous generalization of two different known results given by Hecke-Epstein and Yamamoto.

This result grew out of the study on geodesic multi-dimensional continued fractions and their periodicity. I would like to explain this original motivation after the tea.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/7929