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

Posted in

- Talk [1]

Speaker:

Shingo Sugiyama
Affiliation:

Kyushu University
Date:

Mon, 2017-11-20 14:00 - 14:50 Zagier exhibited an indentity between meromorphic functions as a generalization of the Eichler-Selberg

trace formula for elliptic modular forms. Later, Jacquet and Zagier described such a kind of trace formula

with complex parameter for adelic GL(2), containing abstractness of its spectral and geometric terms. In

this talk, we give a generalization of Zagier's formula to the case of holomorphic Hilbert modular forms

in a new way. As applications, we discuss an equidistribution result for Hecke eigenvalues of Hilbert

modular forms in the level aspect, and the abundant existence of Hilbert modular forms whose

symmetric square L-functions are non-vanishing at points in the critical strip. This is a joint work with

Masao Tsuzuki (Sophia University).

**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/7600