Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus

TL;DR

This paper derives an asymptotic formula with a power-saving error term for the twisted fourth moment of Dirichlet L-functions at a fixed prime power modulus, advancing understanding of their value distribution.

Contribution

It provides the first asymptotic evaluation of the twisted fourth moment for Dirichlet L-functions at a fixed prime power modulus with a power-saving error term.

Findings

Asymptotic formula for the twisted fourth moment established

Power-saving error term achieved in the evaluation

Enhanced understanding of Dirichlet L-functions at fixed moduli

Abstract

We evaluate the twisted four moment on the critical line of the family of Dirichlet $L$-functions to a fixed prime power modulus, obtaining an asymptotic formula with a power saving error term.