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arXiv · 1407.3099

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

J. C. Andrade·J. P. Keating
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Abstract

We extend to the function field setting the heuristic previously developed, by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments and ratios of $L$-functions defined over number fields. Specifically, we give a heuristic for the moments and ratios of a family of $L$-functions associated with hyperelliptic curves of genus $g$ over a fixed finite field $\mathbb{F}_{q}$ in the limit as $g\rightarrow\infty$. Like in the number field case, there is a striking resemblance to the corresponding formulae for the characteristic polynomials of random matrices. As an application, we calculate the one-level density for the zeros of these $L$-functions.

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J. C. Andrade, J. P. Keating. 2014-07-11. Conjectures for the integral moments and ratios of L-functions over function fields. https://doi.org/10.1016/j.jnt.2014.02.019

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