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The distribution of points on superelliptic curves over finite fields

2012/10/01 by Gilyoung Cheong, Melanie Matchett Wood, Cheong, GilYoung +3
Mathematics · #11G20 #11R20 #11R45 #11R58 #11T06 #11T55 #14H25 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1210.0456

openalex publication_date 2012/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give the distribution of points on smooth superelliptic curves over a fixed finite field, as their degree goes to infinity. We also give the distribution of points on smooth m-fold cyclic covers of the line, for any m, as the degree of their superelliptic model goes to infinity. This builds on previous work of Kurlberg, Rudnick, Bucur, David, Feigon, and Lalin for p-fold cyclic covers, but the limits taken differ slightly and the resulting distributions are interestingly different.

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