For a function field
we denote by , resp. , the genus,
resp. the number of
 rational places of . The HasseWeil theorem
gives an upper bound for in terms of and . For large genus, this bound is improved essentially
by the DrinfeldVladut bound.
We present some towers
of function fields
such that the
number of rational places of is close to the DrinfeldVladut bound as
.
The function fields are described explicitly by very simple equations.
(joint work with Arnaldo Garcia and others)
 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 ArtinSchreier extensions of function fields attaining
the DrinfeldVladut bound.
Invent. Math., 121(1):211222, 1995.
 3

Arnaldo Garcia, Henning Stichtenoth, and HansGeorg Rück.
On tame towers over finite fields.
J. Reine Angew. Math., 557:5380, 2003.
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