Preprint A287/2004
Towards a classification of recursive towers of function fields over finite fields

Henning Stichtenoth | Beelen, Peter | Garcia, Arnaldo

**Keywords: **
algebraic curves | finite fields | towers of function fields | recursive towers | asymptotic behaviour

We derive 'normal forms' for the defining equations of recursive towers of function fields over finite fields.Specially interesting are the cases of towers of Kummer type and towers of Artin-Schreier type.We introduce a notion of an f-tower, where f(T) is a rational function on the projective line over the finite field,and we show that several known 'good' towers are indeed f-towers for some f(T).