Abstract
We study the distribution of extreme values of automorphic $L$-functions in a family of holomorphic cusp forms with prime levels. First, we prove an asymptotic formula for a certain density function closely related to this value-distribution. Then we apply it to estimate the probabilities of large deviations for values of automorphic $L$-functions.
Funding Statement
The work of this paper was supported by Grant-in-Aid for JSPS Fellows (Grant Number JP21J00529).
Citation
Masahiro MINE. "Large deviations for values of $L$-functions attached to cusp forms in the level aspect." J. Math. Soc. Japan 75 (3) 941 - 981, July, 2023. https://doi.org/10.2969/jmsj/88888888
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