Abstract:
We give effective bounds on the class number of any algebraic function field of genus gg defined over a finite field. These bounds depend on the possibly partial information on the number of places on each degree r≤gr≤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.
Received:April 12, 2013; in revised form May 12, 2014
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
\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://mathscinet.ams.org/mathscinet-getitem?mr=3427433}
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Linking options:
https://www.mathnet.ru/eng/mmj569
https://www.mathnet.ru/eng/mmj/v15/i3/p425
This publication is cited in the following 3 articles:
Seher TUTDERE, Osmanbey UZUNKOL, “Construction of arithmetic secret sharing schemes by using torsion limits”, Hacettepe Journal of Mathematics and Statistics, 49:2 (2020), 638
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
Lebacque Ph., Zykin A., “on the Number of Rational Points of Jacobians Over Finite Fields”, Acta Arith., 169:4 (2015), 373–384
Citation in format AMSBIB
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