Divisors of Fourier coefficients of modular forms

Abstract

Let $d(n)$ denote the number of divisors of $n$. In this paper, we study the average value of $d(a(p))$, where $p$ is a prime and $a(p)$ is the $p$-th Fourier coefficient of a normalized Hecke eigenform of weight $k\ge 2$ for ${\Gamma }_0(N)$ having rational integer Fourier coefficients.

New York Journal of Mathematics, 2014