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arXiv · 2306.16487

Moments of Artin-Schreier L-functions

Alexandra Florea·Edna Jones·Matilde Lalin
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Abstract

We compute moments of $L$-functions associated to the polynomial family of Artin--Schreier covers over $\mathbb{F}_q$, where $q$ is a power of a prime $p>2$, when the size of the finite field is fixed and the genus of the family goes to infinity. More specifically, we compute the $k^{\text{th}}$ moment for a large range of values of $k$, depending on the sizes of $p$ and $q$. We also compute the second moment in absolute value of the polynomial family, obtaining an exact formula with a lower order term, and confirming the unitary symmetry type of the family.

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Alexandra Florea, Edna Jones, Matilde Lalin. 2023-06-28. Moments of Artin-Schreier L-functions. https://arxiv.org/abs/2306.16487

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