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

Philippe Lebacque; Kohji Matsumoto; Yumiko Umegaki

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arXiv · 2205.00601

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

Philippe Lebacque·Kohji Matsumoto·Yumiko Umegaki

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Abstract

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.

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Philippe Lebacque, Kohji Matsumoto, Yumiko Umegaki. 2022-05-02. On the value-distribution of the logarithms of symmetric square L-functions in the level aspect. https://arxiv.org/abs/2205.00601

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