On lower bounds for the Ihara constants and
AbstractLet $ \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 $A(3)$.
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2002 ◽
Vol 45
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pp. 86-88
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2020 ◽
Vol 63
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pp. 921-936
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2007 ◽
Vol 83
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pp. 14-15
1937 ◽
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(ahead-of-print)
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2014 ◽
Vol 17
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pp. 404-417
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