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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/







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