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

Abstract

In this paper, we establish the expected order of magnitude of the $k$th-moment of quadratic Dirichlet $L$-functions associated to hyperelliptic curves of genus $g$ as well as of prime moduli over a fixed finite field ${\mathbb{F}}_q$ for all real $k\ge 0$.

arXiv comment16 pages

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• Moments of Dirichlet $L$-functions to a fixed modulus over function fields