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 languageEnglish
JournalMoscow Mathematical Journal
Volume15
Issue number1
Pages (from-to)1-29
ISSN1609-3321
Publication statusPublished - 2015

Keywords

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

Cite this

Bassa, A., Beelen, P., Garcia, A., & Stichtenoth, H. (2015). Towers of Function Fields over Non-prime Finite Fields. Moscow Mathematical Journal, 15(1), 1-29.