The mixed second moment of prime quadratic Dirichlet $L$-functions over function fields

TL;DR

This paper derives an asymptotic formula for the mixed second moment of derivatives of quadratic Dirichlet L-functions over function fields, advancing understanding of their value distribution and moments.

Contribution

It provides the first explicit asymptotic formula for the mixed second moment of derivatives of quadratic Dirichlet L-functions in the function field context.

Findings

Asymptotic formula for the mixed second moment derived

Results applicable to the distribution of L-function derivatives

Enhances understanding of moments in function field L-functions

Abstract

We compute an asymptotic formula for the mixed second moment of the $\mu$-th and $\nu$-th derivatives of quadratic Dirichlet $L$-functions over monic, irreducible polynomials in the function field setting.