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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Number of rational points of a singular curve
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by W. A. Zúñiga Galindo PDF
Proc. Amer. Math. Soc. 126 (1998), 2549-2556 Request permission

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
  • 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
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 2549-2556
  • MSC (1991): Primary 11G20; Secondary 14H25
  • DOI: https://doi.org/10.1090/S0002-9939-98-04333-0
  • MathSciNet review: 1451803