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.