English

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

Number Theory 2019-02-20 v4 Algebraic Geometry

Abstract

Let X be a curve over the finite field of q elements and let N(X), g(X) be its number of rational points and genus respectively. The Ihara constant A(q) is defined by the limit superior of N(X)/g(X) as the genus of X goes to infinity. 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).

Keywords

Cite

@article{arxiv.1102.4127,
  title  = {On lower bounds for the Ihara constants A(2) and A(3)},
  author = {Iwan Duursma and Kit-Ho Mak},
  journal= {arXiv preprint arXiv:1102.4127},
  year   = {2019}
}

Comments

22 pages; to appear in Compos. Math