The distribution of points on superelliptic curves over finite fields
Number Theory
2012-10-03 v1
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.
Keywords
Cite
@article{arxiv.1210.0456,
title = {The distribution of points on superelliptic curves over finite fields},
author = {GilYoung Cheong and Melanie Matchett Wood and Azeem Zaman},
journal= {arXiv preprint arXiv:1210.0456},
year = {2012}
}