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On Drinfeld Modular Curves with Many Rational Points over Finite Fields

โœ Scribed by Andreas Schweizer

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
137 KB
Volume
8
Category
Article
ISSN
1071-5797

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โœฆ Synopsis

It is known that Drinfeld modular curves can be used to construct asymptotically optimal towers of curves over finite fields. Using reductions of the Drinfeld modular curves X 0 รฐnรž, we try to find individual curves over finite fields with many rational points. The main idea is to divide by an Atkin-Lehner involution which has many fixed points in order to obtain a quotient with a better ratio #frational pointsg=genus. In a few cases we can improve the known records of rational points.

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