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On the number of rational points on curves over finite fields with many automorphisms

 

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Opened Access On the number of rational points on curves over finite fields with many automorphisms
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Author: Rojas León, Antonio
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2013-01
Published in: Finite Fields and Their Applications, 19 (1), 1-15.
Document type: Article
Abstract: Using Weil descent, we give bounds for the number of rational points on two families of curves over finite fields with a large abelian group of automorphisms: Artin–Schreier curves of the form yq−y=f(x) with f∈Fqr[x], on which the additive group Fq acts, and Kummer curves of the form , which have an action of the multiplicative group . In both cases we can remove a factor from the Weil bound when q is sufficiently large.
Cite: Rojas León, A. (2013). On the number of rational points on curves over finite fields with many automorphisms. Finite Fields and Their Applications, 19 (1), 1-15.
Size: 336.8Kb
Format: PDF

URI: http://hdl.handle.net/11441/42004

DOI: 10.1016/j.ffa.2012.11.001

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