Asymptotically Optimal Towers of Curves over Finite Fields

Ernst-Ulrich Gekeler

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 325-336 from Springer

Abstract: Abstract Let (X k ) k ∈ ℕ be a series of algebraic curves over the finite field $$ \mathbb{F}_q $$ , with N(X k) rational points, and whose genera g(X k) tend to infinity. It is called asymptotically optimal if the ratio N(X k )/g(X k ) tends to its largest possible value q 1/2 - 1. We show that “almost every” such series constructed from (classical elliptic or Drinfeld) modular curves is asymptotically optimal, provided that q is a square.

Keywords: Modular Form; Rational Point; Finite Field; Eisenstein Series; Modular Curve (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18487-1_21

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DOI: 10.1007/978-3-642-18487-1_21

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