On the number of points on abelian and Jacobian varieties over finite fields

Volume 160 / 2013

Yves Aubry, Safia Haloui, Gilles Lachaud Acta Arithmetica 160 (2013), 201-241 MSC: 11G10, 11G20, 11G25, 14G10, 14G15. DOI: 10.4064/aa160-3-1


We give upper and lower bounds for the number of points on abelian varieties over finite fields, and lower bounds specific to Jacobian varieties. We also determine exact formulas for the maximum and minimum number of points on Jacobian surfaces.


  • Yves AubryInstitut de Mathématiques de Luminy
    Aix-Marseille Université
    Institut de Mathématiques de Toulon
    Université du Sud Toulon-Var, France
  • Safia HalouiDepartment of Mathematics
    Technical University of Denmark
    Lyngby, Denmark
  • Gilles LachaudInstitut de Mathématiques de Luminy
    Aix-Marseille Université/CNRS, France

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