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

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.

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.

Received:
Published online:
DOI: 10.5802/jtnb.809
Classification: 14H05,  12E20
Keywords: Finite field, function field, class number
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Stéphane Ballet; Robert  Rolland. Lower bounds on the class number of algebraic function fields defined over any finite field. Journal de Théorie des Nombres de Bordeaux, Volume 24 (2012) no. 3, pp. 505-540. doi : 10.5802/jtnb.809. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.809/

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