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On the number of rational points of Jacobians over finite fields

Abstract : In this article we prove lower and upper bounds for class numbers of algebraic curves defined over finite fields. These bounds turn out to be better than most of the previously known bounds obtained using combinatorics. The methods used in the proof are essentially those from the explicit asymptotic theory of global fields. We thus provide a concrete application of effective results from the asymptotic theory of global fields and their zeta-functions.
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https://hal.archives-ouvertes.fr/hal-01689002
Contributor : Alicia Benson-Rumiz Connect in order to contact the contributor
Submitted on : Saturday, January 20, 2018 - 1:47:46 AM
Last modification on : Monday, November 15, 2021 - 7:30:02 PM

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Philippe Lebacque, Alexey Zykin. On the number of rational points of Jacobians over finite fields. Acta Arithmetica, 2015, 169 (4), pp.373-384. ⟨10.4064/aa169-4-5⟩. ⟨hal-01689002⟩

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