Distribution of Points on Cyclic Curves over Finite Fields

2015/11/24 by Meisner, Patrick
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1511.07814

Abstract

We determine in this paper the distribution of the number of points on the cyclic covers of ℙ¹(\mathbbF_q) with affine models C: Y^r = F(X), where F(X) ∈ \mathbbF_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 \mathbbF_q. In all cases, the distribution is given by a sum of random variables.

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