1 results
On lower bounds for the Ihara constants
$A(2)$ and 
$A(3)$
- Part of
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- Journal:
- Compositio Mathematica / Volume 149 / Issue 7 / July 2013
- Published online by Cambridge University Press:
- 03 May 2013, pp. 1108-1128
- Print publication:
- July 2013
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- Article
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Let
$ \mathcal{X} $ be a curve over 
${ \mathbb{F} }_{q} $ and let 
$N( \mathcal{X} )$, 
$g( \mathcal{X} )$ be its number of rational points and genus respectively. The Ihara constant 
$A(q)$ is defined by 
$A(q)= {\mathrm{lim~sup} }_{g( \mathcal{X} )\rightarrow \infty } N( \mathcal{X} )/ g( \mathcal{X} )$. 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 
$A(3)$.
