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 $k\ge 0$.

16 pages

References in corpus (4)

• 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
• Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli
• Bounds for moments of cubic and quartic Dirichlet $L$-functions

Cited by in corpus (1)

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