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

Iwan Duursma; Kit Ho Mak

doi:10.1112/S0010437X12000796

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

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Abstract

Let χ be a curve over F_q 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 language	English (US)
Pages (from-to)	1108-1128
Number of pages	21
Journal	Compositio Mathematica
Volume	149
Issue number	7
DOIs	https://doi.org/10.1112/S0010437X12000796
State	Published - Jul 2013

Keywords

Asymptotic bound
Curves with many points
Ihara constant

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.1112/S0010437X12000796

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

Abstract

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