A spectral universality theorem for Maass $L$-functions

Giacomo Cherubini; Alberto Perelli

A spectral universality theorem for Maass $L$-functions

Number Theory 2019-10-01 v2

Authors: Giacomo Cherubini , Alberto Perelli

Abstract

We show that for a positive proportion of Laplace eigenvalues $\lambda_j$ 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.

Keywords

laplacian eigenfunctions l-functions harmonic functions

Cite

@article{arxiv.1811.02498,
  title  = {A spectral universality theorem for Maass $L$-functions},
  author = {Giacomo Cherubini and Alberto Perelli},
  journal= {arXiv preprint arXiv:1811.02498},
  year   = {2019}
}

Comments

12 pages, final version, corrected typos

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