Probability density functions attached to random Euler products for automorphic $L$-functions

Abstract

In this paper, we study the value-distributions of $L$-functions of holomorphic primitive cusp forms in the level aspect. We associate such automorphic $L$-functions with probabilistic models called the random Euler products. First, we prove the existence of probability density functions attached to the random Euler products. Then various mean values of automorphic $L$-functions are expressed as integrals involving the density functions. Moreover, we estimate the discrepancies between the distributions of values of automorphic $L$-functions and those of the random Euler products.

38 pages

References in corpus (2)

• Lower bounds for moments of L-functions: symplectic and orthogonal examples
• An M-function associated with Goldbach's problem

Cited by in corpus (2)

• Large deviations for values of $L$-functions attached to cusp forms in the level aspect
• The value-distribution of Artin $L$-functions associated with cubic fields in conductor aspect