The quantitative distribution of Hecke eigenvalues of Maass forms

Abstract

Let $f$ be a normalized Hecke-Maass cusp form of weight zero for the group $S{L}_2(\mathbb{Z})$. This article presents several quantitative results about the distribution of Hecke eigenvalues of $f$. Applications to the ${\Omega }_{\pm }$-results for the Hecke eigenvalues of $f$ and its symmetric square sym${}^2(f)$ are also given.