Lower bounds on the class number of algebraic function fields defined over any finite field
Stéphane Ballet, Robert Rolland · Journal de Théorie des Nombres de Bordeaux · 2012
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.