Rudnick and Soundararajan's Theorem for Function Fields

Abstract

In this paper we prove a function field version of a theorem by Rudnick and Soundararajan about lower bounds for moments of quadratic Dirichlet $L$-functions. We establish lower bounds for the moments of quadratic Dirichlet $L$--functions associated to hyperelliptic curves of genus $g$ over a fixed finite field ${\mathbb{F}}_q$ in the large genus $g$ limit.

18 pages, to appear in Finite Fields and Their Applications

References in corpus (4)

• Continuous lower bounds for moments of zeta and L-functions
• The Mean Value of $L(\frac{1}{2},\chi )$ in the Hyperelliptic Ensemble
• Conjectures for the integral moments and ratios of L-functions over function fields
• Statistics of the zeros of zeta functions in families of hyperelliptic curves over a finite field

Cited by in corpus (1)

• Moments of quadratic Dirichlet $L$-functions over Function Fields