On the value-distribution of the logarithms of symmetric square L-functions in the level aspect

Philippe Lebacque, Kohji Matsumoto, Yumiko Umegaki

Published 2022-05-02Version 1

We consider the value distribution of logarithms of symmetric square L-functions associated with newforms of even weight and prime power level at real s> 1/2. We prove that certain averages of those values can be written as integrals involving a density function which is related with the Sato-Tate measure. Moreover, we discuss the case of symmetric power L-functions.