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

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

2011-02-21

arxiv.org/abs/1102.4127v3

Mathematics

Number Theory

22 pages

Scientific paper

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 fi?eld tower method to obtain an improvement of the best known lower bounds on A(2) and A(3).

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