# Henning Stichtenoth: Towers of algebraic function fields

For a function field we denote by , resp. , the genus, resp. the number of - rational places of . The Hasse-Weil theorem gives an upper bound for in terms of and . For large genus, this bound is improved essentially by the Drinfeld-Vladut bound. We present some towers of function fields such that the number of rational places of is close to the Drinfeld-Vladut bound as . The function fields are described explicitly by very simple equations. (joint work with Arnaldo Garcia and others)

## Bibliography

1
Juscelino Bezerra, Arnaldo Garcia, and Henning Stichtenoth.
An explicit tower of function fields over cubic finite fields and Zink's lower bound.
(preprint), 2004.

2
Arnaldo Garcia and Henning Stichtenoth.
A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound.
Invent. Math., 121(1):211-222, 1995.

3
Arnaldo Garcia, Henning Stichtenoth, and Hans-Georg Rück.
On tame towers over finite fields.
J. Reine Angew. Math., 557:53-80, 2003.