On the occurrence of large positive Hecke eigenvalues for GL(2)

Abstract

Let $\pi$ be a cuspidal automorphic representation for GL(2)/$\mathbb{Q}$ that is self-dual. In this Note we show that there exists a positive upper Dirichlet density of primes at which the associated Hecke eigenvalues of $\pi$ are larger than a specified positive constant.

arXiv commentFinal version. 8 pages