Large deviations for values of 𝐿-functions attached to cusp forms in the level aspect

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.