Towers of Function Fields over Non-prime Finite Fields

Alp Bassa; Peter  Beelen; Arnaldo Garcia; Henning  Stichtenoth

Towers of Function Fields over Non-prime Finite Fields

Alp Bassa, Peter Beelen, Arnaldo Garcia, Henning Stichtenoth

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Abstract

Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara’s quantity A(ℓ), for ℓ = pⁿ with p prime and n > 3 odd. We relate the explicit equations to Drinfeld modular varieties.

Original language	English
Journal	Moscow Mathematical Journal
Volume	15
Issue number	1
Pages (from-to)	1-29
ISSN	1609-3321
Publication status	Published - 2015

Keywords

Curves with many points
Towers of function fields
Genus
Rational places
Ihara’s constant

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T1 - Towers of Function Fields over Non-prime Finite Fields

AU - Bassa, Alp

AU - Beelen, Peter

AU - Garcia, Arnaldo

AU - Stichtenoth, Henning

PY - 2015

Y1 - 2015

N2 - Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara’s quantity A(ℓ), for ℓ = pn with p prime and n > 3 odd. We relate the explicit equations to Drinfeld modular varieties.

AB - Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara’s quantity A(ℓ), for ℓ = pn with p prime and n > 3 odd. We relate the explicit equations to Drinfeld modular varieties.

KW - Curves with many points

KW - Towers of function fields

KW - Genus

KW - Rational places

KW - Ihara’s constant

M3 - Journal article

SN - 1609-3321

VL - 15

SP - 1

EP - 29

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

IS - 1

ER -

Towers of Function Fields over Non-prime Finite Fields

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