On lower bounds for the Ihara constants A(2) and A(3)

Iwan Duursma, Kit Ho Mak

Research output: Contribution to journalArticlepeer-review


Let χ be a curve over Fq and let N(χ), g(χ) be its number of rational points and genus respectively. The Ihara constant A(q) is defined by A(q)=lim g(χ) →∞N(χ)/g(χ).In this paper, we employ a variant of Serre's class field tower method to obtain an improvement of the best known lower bounds on A(2) and A(3).

Original languageEnglish (US)
Pages (from-to)1108-1128
Number of pages21
JournalCompositio Mathematica
Issue number7
StatePublished - Jul 2013


  • Asymptotic bound
  • Curves with many points
  • Ihara constant

ASJC Scopus subject areas

  • Algebra and Number Theory


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