Explicit trace formulas for symmetric square L-functions for GL(2) and some applications

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).