Moscow Mathematical Journal

Volume 15, Issue 1, January–March 2015 pp. 1–29.

Towers of Function Fields over Non-prime Finite Fields

Authors: Alp Bassa (1), Peter Beelen (2), Arnaldo Garcia (3), and Henning Stichtenoth (4)
Author institution:(1) Sabancı University, MDBF, 34956 Tuzla, İstanbul, Turkey
(2) Technical University of Denmark, Department of Applied Mathematics and Computer Science, Matematiktorvet, Building 303B, DK-2800, Lyngby, Denmark
(3) Instituto Nacional de Matemática Pura e Aplicada, IMPA, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, RJ, Brazil
(4) Sabancı University, MDBF, 34956 Tuzla, İstanbul, Turkey

Summary:

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.

2010 Math. Subj. Class. 11G20, 11G09, 11R58.

Keywords: Curves with many points, towers of function fields, genus, rational places, Ihara's constant.

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