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Mosc. Math. J., 2015, Volume 15, Number 4, Pages 615–627 (Mi mmj577)  

This article is cited in 1 scientific paper (total in 1 paper)

On the maximum number of rational points on singular curves over finite fields

Yves Aubryab, Annamaria Iezzia

a Institut de Mathématiques de Marseille, CNRS-UMR 7373, Aix-Marseille Université, France
b Institut de Mathématiques de Toulon, Université de Toulon, France

Abstract: We give a construction of singular curves with many rational points over finite fields. This construction enables us to prove some results on the maximum number of rational points on an absolutely irreducible projective algebraic curve defined over $\mathbb F_q$ of geometric genus $g$ and arithmetic genus $\pi$.

Key words and phrases: singular curves, finite fields, rational points, zeta function.

Funding Agency Grant Number
Agence Nationale de la Recherche ANR-11-LABX- 0033
ANR-11-IDEX-0001-02
This work has been carried out in the framework of the Labex Archiméde (ANR-11-LABX-0033) and of the A*MIDEX project (ANR-11-IDEX-0001-02), funded by the "Investissements d'Avenir" French Government programme managed by the French National Research Agency (ANR).


DOI: https://doi.org/10.17323/1609-4514-2015-15-4-615-627

Full text: http://www.mathjournals.org/.../2015-015-004-003.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 14H20, 11G20, 14G15
Received: January 15, 2015; in revised form August 17, 2015
Language:

Citation: Yves Aubry, Annamaria Iezzi, “On the maximum number of rational points on singular curves over finite fields”, Mosc. Math. J., 15:4 (2015), 615–627

Citation in format AMSBIB
\Bibitem{AubIez15}
\by Yves~Aubry, Annamaria~Iezzi
\paper On the maximum number of rational points on singular curves over finite fields
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 4
\pages 615--627
\mathnet{http://mi.mathnet.ru/mmj577}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-4-615-627}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3438824}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000368530900003}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Y. Aubry, A. Iezzi, “Optimal and maximal singular curves”, Arithmetic, Geometry, Cryptography and Coding Theory, Contemporary Mathematics, 686, eds. A. Bassa, A. Couvreur, D. Kohel, Amer. Math. Soc., 2017, 31–43  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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