The fourth moment of holomorphic Hecke cusp forms in shorter intervals

TL;DR

This paper investigates the average fourth moment of holomorphic Hecke cusp forms within shorter intervals of weights, extending previous results and providing new insights into their distribution.

Contribution

It introduces a refined analysis of the fourth moment of holomorphic Hecke cusp forms over shorter weight intervals, improving upon earlier bounds by Khan.

Findings

Established the average fourth moment in shorter intervals of weight.

Improved bounds on the fourth moment compared to previous work.

Enhanced understanding of the distribution of holomorphic Hecke cusp forms.

Abstract

Let $0<c\le 1/4$ be fixed. For $H = K^{\frac{3}{4}+ c}$, we find the average value of the fourth moment of holomorphic Hecke cusp forms of weight varies within $[K,K+H]$, improving a previous result of Khan.