On Products of Fourier Coefficients of Cusp Forms

Abstract

The purpose of this paper is to study products of Fourier coefficients of an elliptic cusp form, $a(n)a(n+r)$ $(n\ge 1)$ for a fixed positive integer $r$, concerning both non-vanishing and non-negativity.

Minor revision: Several typos fixed, notation made more consistent. To appear in Forum Math