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

Abstract

In this paper, we establish the expected order of magnitude of the kth-moment of quadratic Dirichlet Lfunctions associated to hyperelliptic curves of genus g as well as of prime moduli over a fixed finite field Fq for all real k ≥ 0.

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

“…(2.5) Proof. The formulas (2.2)-(2.4) can be found in [14,Lemma 2.2]. Hence it only reamins to establish (2.5).…”