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Curves of every genus with a prescribed number of rational points

✍ Scribed by Nurdagül Anbar, Henning Stichtenoth

Book ID
120915306
Publisher
Springer
Year
2013
Tongue
English
Weight
233 KB
Volume
44
Category
Article
ISSN
1678-7714

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Let N q g denote the maximal number of F q -rational points on any curve of genus g over F q . Ihara (for square q) and Serre (for general q) proved that lim sup g→∞ N q g /g > 0 for any fixed q. Here we prove lim g→∞ N q g = ∞. More precisely, we use abelian covers of P 1 to prove lim inf g→∞ N q g