Lower bounds on the class number of algebraic function fields defined over any finite field
Journal de théorie des nombres de Bordeaux, Tome 24 (2012) no. 3, pp. 505-540.

Nous donnons des bornes inférieures sur le nombre de diviseurs effectifs de degré g-1 par rapport au nombre de places d’un certain degré d’un corps de fonctions algébriques de genre g défini sur un corps fini. Nous déduisons des bornes inférieures du nombre de classes qui améliorent les bornes de Lachaud-Martin-Deschamps et des bornes inférieures asymptotiques atteignant celles de Tsfasman-Vladut. Nous donnons des exemples de tours de corps de fonctions algébriques ayant un grand nombre de classes.

We give lower bounds on the number of effective divisors of degree g-1 with respect to the number of places of certain degrees of an algebraic function field of genus g defined over a finite field. We deduce lower bounds for the class number which improve the Lachaud - Martin-Deschamps bounds and asymptotically reaches the Tsfasman-Vladut bounds. We give examples of towers of algebraic function fields having a large class number.

DOI : 10.5802/jtnb.809
Classification : 14H05, 12E20
Mots clés : Finite field, function field, class number
Ballet, Stéphane 1 ; Rolland, Robert 1

1 Aix-Marseille Université Institut de Mathématiques de Luminy Équipe Arithmétique et Théorie de l’Information et Groupe d’Études et Recherche en Informatique des Systèmes Communicants Sécurisés. Case 907 F13288 Marseille cedex 9 France
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Ballet, Stéphane;  Rolland, Robert. Lower bounds on the class number of algebraic function fields defined over any finite field. Journal de théorie des nombres de Bordeaux, Tome 24 (2012) no. 3, pp. 505-540. doi : 10.5802/jtnb.809. http://archive.numdam.org/articles/10.5802/jtnb.809/

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