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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Number of rational points of a singular curve


Author: W. A. Zúñiga Galindo
Journal: Proc. Amer. Math. Soc. 126 (1998), 2549-2556
MSC (1991): Primary 11G20; Secondary 14H25
MathSciNet review: 1451803
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Abstract: In this paper, we give a bound for the number of rational points of a complete, geometrically irreducible, algebraic curve defined over a finite field. We compare it with other known bounds and discuss its sharpness. We also show that the asymptotic Drinfeld-Vladut bound can be generalized to the case of singular curves.


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Additional Information

W. A. Zúñiga Galindo
Affiliation: Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, CEP 22460-320, Rio de Janeiro-R.J., Brazil
Address at time of publication: Universidad Autónoma de Bucaramanga, Laboratorio de Computo Especializado, A.A.1642, Bucaramanga, Colombia
Email: wzuniga@bumanga.unab.edu.co

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04333-0
PII: S 0002-9939(98)04333-0
Received by editor(s): October 17, 1995
Received by editor(s) in revised form: January 31, 1997
Additional Notes: The author thanks Prof. Karl-Otto Stöhr for many helpful discussions, and the referee for his or her useful comments. Supported by CNPq-Brazil and COLCIENCIAS-Colombia
Communicated by: William W. Adams
Article copyright: © Copyright 1998 American Mathematical Society