The fifth moment of Hecke L-functions in the weight aspect

TL;DR

This paper establishes a sharp upper bound for the fifth moment of Hecke L-functions linked to holomorphic cusp forms of full level and varying weight, advancing understanding in analytic number theory.

Contribution

It provides the first sharp upper bound for the fifth moment of Hecke L-functions in the weight aspect, assuming Selberg's eigenvalue conjecture.

Findings

Proves a sharp upper bound for the fifth moment of Hecke L-functions.

The bound is asymptotically optimal under Selberg's eigenvalue conjecture.

Enhances understanding of moments of L-functions in the weight aspect.

Abstract

We prove an upper bound for the fifth moment of Hecke L-functions associated to holomorphic Hecke cusp forms of full level and weight k in a dyadic interval K < k < 2K, as K tends to infinity. The bound is sharp on Selberg's eigenvalue conjecture.