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The distribution of points on curves over finite fields in some small rectangles

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Abstract

Let \(p\) be a prime. We study the distribution of points on a class of curves \(C\) over \(\mathbb{F }_p\) inside very small rectangles \(\mathcal{B }\) for which the Weil bound fails to give nontrivial information. In particular, we show that the distribution of points on \(C\) over long rectangles is Gaussian.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA, 30332-0160, USA

    Kit-Ho Mak

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  1. Kit-Ho Mak
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Correspondence to Kit-Ho Mak.

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Communicated by J. Schoißengeier.

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Mak, KH. The distribution of points on curves over finite fields in some small rectangles. Monatsh Math 174, 577–586 (2014). https://doi.org/10.1007/s00605-013-0572-4

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  • DOI: https://doi.org/10.1007/s00605-013-0572-4

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