A spectral universality theorem for Maass L-functions

Abstract

We show that for a positive proportion of Laplace eigenvalues λ j , the associated Hecke-Maass L-functions L(s, u j ) approximate with arbitrary precision any target function f (s) on a closed disc with center in 3/4 and radius r < 1/4. The main ingredients in the proof are the spectral large sieve of Deshouillers-Iwaniec and Sarnak's equidistribution theorem for Hecke eigenvalues.