The shifted fourth moment of automorphic L-functions of prime power level

TL;DR

This paper establishes the asymptotic behavior of the fourth moment of automorphic L-functions at prime power levels, extending previous work on lower moments and prime levels to a broader class of levels.

Contribution

It generalizes the asymptotic formulas for the fourth moment of automorphic L-functions to prime power levels, building on prior results for lower moments and prime levels.

Findings

Proves the asymptotic formula for the fourth moment at prime power levels.

Extends previous results from prime levels to prime power levels.

Provides a foundation for further statistical analysis of automorphic L-functions.

Abstract

We prove the asymptotic formula for the fourth moment of automorphic $L$-functions of level $p^{\nu}$, where $p$ is a fixed prime number and $\nu \rightarrow \infty$. This paper is a continuation of work by Rouymi, who computed asymptotics of the first three moments at prime power level, and a generalization of results obtained for prime level by Duke, Friedlander & Iwaniec and Kowalski, Michel & Vanderkam.