A survey on recursive towers and Ihara's constant

Abstract

Since Serre gave his famous Harvard lectures in 1985 on various aspects of the theory of algebraic curves defined over a finite field, there have been many developments. In this survey article, an overview will be given on the developments concerning the quantity $A(q)$, known as Ihara's constant. The main focus will be on explicit techniques and in particular recursively defined towers of function fields over a finite field, which have given good lower bounds for Ihara's constant in the past.