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 , p. 505-540
MR 3010627 | Zbl 1273.14052
doi : 10.5802/jtnb.809
URL stable : http://www.numdam.org/item?id=JTNB_2012__24_3_505_0

Classification:  14H05,  12E20
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.

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