Sharp Bound for the Fourth Moment of Holomorphic Hecke Cusp Forms

Abstract

Abstract We prove that the fourth moment of holomorphic Hecke cusp forms is bounded by a constant provided that the Generalized Riemann Hypothesis holds. We accomplish this using Watson’s formula, which translates the question in hand into a moment problem for $L$-functions that is amenable to the techniques of Soundararajan and Harper on obtaining sharp bounds for moments of the Riemann zeta function.