Conjectures for the Integral Moments and Ratios of L-functions in Even characteristic

Abstract

In this paper, we extend to the function field setting the heuristics developed by Conrey, Farmer, Keating, Rubinstein and Snaith for the integral moments of L-functions. Also, we adapt to function field setting the heuristics first developed by Conrey, Farmer and Zirnbauer to the study of mean values of ratios of L-functions. Specifically, we obtain an asymptotic formula for the integral moments and ratios of the quadratic Dirichlet L-functions $L(s,{\chi }_u)$ over the rational function field ${\mathbb{F}}_q(T)$, when $q$ is a power of 2 and over a given family. As an application, we calculate the one-level density for the zeros of these L-functions.

37 pages, Comments are welcome. arXiv admin note: text overlap with arXiv:1407.3099 by other authors

References in corpus (1)

• Conjectures for the integral moments and ratios of L-functions over function fields