Rudnick and Soundararajan's Theorem for Function Fields

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.