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arXiv · 1803.03511

Divisibility of L-Polynomials for a Family of Artin-Schreier Curves

Gary McGuire·Emrah Sercan Yılmaz
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Abstract

In this paper we consider the curves $C_k^{(p,a)} : y^p-y=x^{p^k+1}+ax$ defined over $\mathbb F_p$ and give a positive answer to a conjecture about a divisibility condition on $L$-polynomials of the curves $C_k^{(p,a)}$. Our proof involves finding an exact formula for the number of $\mathbb F_{p^n}$-rational points on $C_k^{(p,a)}$ for all $n$, and uses a result we proved elsewhere about the number of rational points on supersingular curves.

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Gary McGuire, Emrah Sercan Yılmaz. 2018-03-09. Divisibility of L-Polynomials for a Family of Artin-Schreier Curves. https://arxiv.org/abs/1803.03511

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