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

Kit-Ho Mak

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

Number Theory 2013-04-22 v1 Algebraic Geometry

Authors: Kit-Ho Mak

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 $B$ for which the Weil bound fails to give nontrivial information. In particular, we show that the distribution of points on $C$ over some long rectangles is Gaussian.

Keywords

finite fields curves point distribution Weil bound Gaussian distribution

Cite

@article{arxiv.1304.5272,
  title  = {The distribution of points on curves over finite fields in some small rectangles},
  author = {Kit-Ho Mak},
  journal= {arXiv preprint arXiv:1304.5272},
  year   = {2013}
}

Comments

7 pages

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