The distribution of points on superelliptic curves over finite fields

DOI10.1090/S0002-9939-2014-12218-0zbMATH Open1408.11063arXiv1210.0456MaRDI QIDQ5179305

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Publication date: 19 March 2015

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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.

Full work available at URL: https://arxiv.org/abs/1210.0456

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