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:
https://doi.org/10.1090/S0002-9939-98-04333-0

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