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