Towers of Function Fields over Non-prime Finite Fields

By A. Bassa, Peter Beelen, Arnaldo Garcia, Henning Stichtenoth. 2012

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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 $A(\ell)$, for $\ell = p^n$ with $p$ prime and $n>3$ odd. We relate the explicit equations to Drinfeld modular varieties.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/603b2d6a9099d6ba1c0b67b7e64d4f7ce3c73199