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arXiv · 2110.00477

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

J. MacMillan
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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.

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J. MacMillan. 2021-10-01. Conjectures for the Integral Moments and Ratios of L-functions in Even characteristic. https://arxiv.org/abs/2110.00477

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