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On the number of rational points of Jacobians over finite fields

Volume 169 / 2015

Philippe Lebacque, Alexey Zykin Acta Arithmetica 169 (2015), 373-384 MSC: Primary 11R29; Secondary 11R58. DOI: 10.4064/aa169-4-5


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.


  • Philippe LebacqueLaboratoire de Mathématiques de Besançon
    Université de Franche-Comté
    16, route de Gray
    25030 Besançon Cedex, France
    Inria Saclay-Ile-de-France
    équipe-projet Grace
  • Alexey ZykinLaboratoire GAATI
    Université de la Polynésie française
    BP 6570 98702 Faa'a, Tahiti, French Polynesia
    National Research University
    Higher School of Economics
    AG Laboratory, HSE
    7 Vavilova St.
    Moscow 117312, Russia
    Laboratoire Poncelet (UMI 2615)
    Institute for Information Transmission Problems
    Russian Academy of Sciences

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