# On the number of rational points on curves over finite fields with many automorphisms - Mathematics > Algebraic Geometry

On the number of rational points on curves over finite fields with many automorphisms - Mathematics > Algebraic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: Using Weil descent, we give bounds for the number of rational points on twofamilies of curves over finite fields with a large abelian group ofautomorphisms: Artin-Schreier curves of the form $y^q-y=fx$ with$f\in\Fqrx$, on which the additive group $\Fq$ acts, and Kummer curves of theform $y^{\frac{q-1}{e}}=fx$, which have an action of the multiplicative group$\Fq^\star$. In both cases we can remove a $\sqrt{q}$ factor from the Weilbound when $q$ is sufficiently large.

Author: ** Antonio Rojas-Leon**

Source: https://arxiv.org/