Minorations du nombre de classes des corps de fonctions algébriques définis sur un corps fini

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• 作者：St&#xe9 ; phane Ballet^a ; ^{stephane.ballet@univmed.fr"" rel=""nofollow} ; Robert Rolland^a ; ^{robert.rolland@acrypta.fr"" rel=""nofollow}
• 刊名：Comptes Rendus Mathematique
• 出版年：2011
• 出版时间：July 2011
• 年：2011
• 卷：349
• 期：13-14
• 页码：709-712
• 全文大小：131 K

文摘

We give lower bounds for the number of effective divisors of degree g−1 of an algebraic function field of one variable of genus g2 defined over a finite field. We deduce lower bounds for the class number, depending mainly on the number of places of a certain degree, which improve the best known lower bounds in many cases. Moreover, we prove that any family of algebraic function fields having asymptotically (with respect to the genus) a large number of places of a certain degree r1, have a large asymptotical class number for which we give an estimate.