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arXiv · 1511.07814

Distribution of Points on Cyclic Curves over Finite Fields

Patrick Meisner
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Abstract

We determine in this paper the distribution of the number of points on the cyclic covers of $\mathbb{P}^1(\mathbb{F}_q)$ with affine models $C: Y^r = F(X)$, where $F(X) \in \mathbb{F}_q[X]$ and $r^{th}$-power free when $q$ is fixed and the genus, $g$, tends to infinity. This generalize the work of Kurlberg and Rudnick and Bucur, David, Feigon and Lalin who considered different families of curves over $\mathbb{F}_q$. In all cases, the distribution is given by a sum of random variables.

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Patrick Meisner. 2015-11-24. Distribution of Points on Cyclic Curves over Finite Fields. https://arxiv.org/abs/1511.07814

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