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 Mosc. Math. J., 2015, Volume 15, Number 4, Pages 653–677 (Mi mmj579)

Effective bounds on class number and estimation for any step of towers of algebraic function fields over finite fields

S. Balleta, R. Rollanda, S. Tutdereb

a Aix-Marseille Université, Institut de Mathématiques de Luminy, case 930, F13288 Marseille cedex 9, France
b Gebze Technical University, Department of Mathematics, Gebze, Kocaeli, Turkey

Abstract: We give new effective bounds on the class number of an algebraic function field defined over a finite field. Then we give significant examples of towers of algebraic function fields having a large class number. In particular, we estimate the genus, the number of places and the class number of function fields which are steps of towers having one or several positive Tsfasman–Vlăduţ invariants. Note that the study is not done asymptotically, but for each individual step of the towers for which we determine precise parameters.

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

DOI: https://doi.org/10.17323/1609-4514-2015-15-4-653-677

Full text: http://www.mathjournals.org/.../2015-015-004-005.html
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Bibliographic databases:

MSC: Primary 14H05; Secondary 12E20
Received: February 9, 2015; in revised form June 29, 2015
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Citation: 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

Citation in format AMSBIB
\Bibitem{BalRolTut15} \by S.~Ballet, R.~Rolland, S.~Tutdere \paper Effective bounds on class number and estimation for any step of towers of algebraic function fields over finite fields \jour Mosc. Math.~J. \yr 2015 \vol 15 \issue 4 \pages 653--677 \mathnet{http://mi.mathnet.ru/mmj579} \crossref{https://doi.org/10.17323/1609-4514-2015-15-4-653-677} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3438826} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000368530900005}