Preprint A709/2012
Towers of Function Fields over Non-prime Finite Fields

Peter Beelen | Garcia, Arnaldo | Stichtenoth, Henning | Bassa, Alp

**Keywords: **
function fields | finite fields | rational places | genus | asymptotics | Ihara quantity

Over all non-prime finite fields, we construct some recursive towers of function fields with
many rational places. Thus we obtain a substantial improvement on all known lower bounds
for Ihara's quantity A(l), for l = p^n with p prime and n > 3 an odd integer. A Drinfeld modular interpretation
of the towers is given as well.