The Fourth Moment of Dirichlet L-Functions for the Rational Function Field

TL;DR

This paper investigates the behavior of Dirichlet L-functions over polynomial rings in finite fields, deriving an asymptotic formula for their fourth moment and establishing bounds for higher moments.

Contribution

It provides the first asymptotic formula for the fourth moment of Dirichlet L-functions over finite fields and bounds for their higher moments.

Findings

Asymptotic formula for the fourth moment established

Lower bounds for the 2kth moments derived

Enhanced understanding of L-functions in finite field context

Abstract

We study the moments of the Dirichlet L-function when defined over the polynomial ring over finite fields. We find an asymptotic formula to the fourth moment of the central value of Dirichlet L functions in this context. We also find a lower bound to the 2kth moment of these L-functions.