Geodesic
On the number of rational points of Jacobians over finite fields
Philippe Lebacque 1   ; Alexey Zykin 2
1 Laboratoire de Mathématiques de Besançon Université de Franche-Comté 16, route de Gray 25030 Besançon Cedex, France and Inria Saclay-Ile-de-France équipe-projet Grace
2 Laboratoire GAATI Université de la Polynésie française BP 6570 98702 Faa'a, Tahiti, French Polynesia and National Research University Higher School of Economics AG Laboratory, HSE 7 Vavilova St. Moscow 117312, Russia and Laboratoire Poncelet (UMI 2615) and Institute for Information Transmission Problems Russian Academy of Sciences
Acta Arithmetica, Tome 169 (2015) no. 4, pp. 373-384 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We prove lower and upper bounds for the 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.
DOI : 10.4064/aa169-4-5
Keywords: prove lower upper bounds class numbers algebraic curves defined finite fields these bounds turn out better previously known bounds obtained using combinatorics methods proof essentially those explicit asymptotic theory global fields provide concrete application effective results asymptotic theory global fields their zeta functions

Philippe Lebacque  1   ; Alexey Zykin  2

1 Laboratoire de Mathématiques de Besançon Université de Franche-Comté 16, route de Gray 25030 Besançon Cedex, France and Inria Saclay-Ile-de-France équipe-projet Grace
2 Laboratoire GAATI Université de la Polynésie française BP 6570 98702 Faa'a, Tahiti, French Polynesia and National Research University Higher School of Economics AG Laboratory, HSE 7 Vavilova St. Moscow 117312, Russia and Laboratoire Poncelet (UMI 2615) and Institute for Information Transmission Problems Russian Academy of Sciences 
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     author = {Philippe Lebacque and Alexey Zykin},
     title = {On the number of rational points of {Jacobians} over finite fields},
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Philippe Lebacque; Alexey Zykin. On the number of rational points of Jacobians over finite fields. Acta Arithmetica, Tome 169 (2015) no. 4, pp. 373-384. doi: 10.4064/aa169-4-5

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