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Mosc. Math. J., 2015, Volume 15, Number 3, Pages 425–433 (Mi mmj569)  

This article is cited in 2 scientific papers (total in 2 papers)

Lower bounds on the number of rational points of Jacobians over finite fields and application to algebraic function fields in towers

S. Balleta, R. Rollanda, S. Tutdereb

a Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France, case 907, 163 Avenue de Luminy, 13288 Marseille Cedex 9
b Department of Mathematics, Gebze Institute of Technology, Gebze, Kocaeli, Turkey

Abstract: We give effective bounds on the class number of any algebraic function field of genus $g$ defined over a finite field. These bounds depend on the possibly partial information on the number of places on each degree $r\leq g$. Such bounds are especially useful for estimating the class numbers of function fields in towers of function fields over finite fields having several positive Tsfasman–Vlăduţ invariants.

Key words and phrases: finite field, Jacobian, algebraic function field, class number, tower.

DOI: https://doi.org/10.17323/1609-4514-2015-15-3-425-433

Full text: http://www.mathjournals.org/.../2015-015-003-002.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 14H05; Secondary 12E20
Received: April 12, 2013; in revised form May 12, 2014
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Citation: S. Ballet, R. Rolland, S. Tutdere, “Lower bounds on the number of rational points of Jacobians over finite fields and application to algebraic function fields in towers”, Mosc. Math. J., 15:3 (2015), 425–433

Citation in format AMSBIB
\Bibitem{BalRolTut15}
\by S.~Ballet, R.~Rolland, S.~Tutdere
\paper Lower bounds on the number of rational points of Jacobians over finite fields and application to algebraic function fields in towers
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 3
\pages 425--433
\mathnet{http://mi.mathnet.ru/mmj569}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-3-425-433}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3427433}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000365392600002}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. Ballet, R. Rolland, S. Tutdere, “Effective bounds on class number and estimation for any step of towers of algebraic function fields over finite fields”, Mosc. Math. J., 15:4 (2015), 653–677  mathnet  crossref  mathscinet
    2. Lebacque Ph., Zykin A., “on the Number of Rational Points of Jacobians Over Finite Fields”, Acta Arith., 169:4 (2015), 373–384  crossref  mathscinet  zmath  isi  elib  scopus
  • Moscow Mathematical Journal
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