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)
- 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.
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