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

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.

7 pages

References in corpus (1)

• The distribution of rational points and polynomial maps on an affine variety over a finite field on average