The Cohen–Lenstra heuristics, moments and $p^j$-ranks of some groups

Volume 164 / 2014

Christophe Delaunay, Frédéric Jouhet Acta Arithmetica 164 (2014), 245-263 MSC: 11R29, 11G05. DOI: 10.4064/aa164-3-3


This article deals with the coherence of the model given by the Cohen–Lenstra heuristic philosophy for class groups and also for their generalizations to Tate–Shafarevich groups. More precisely, our first goal is to extend a previous result due to É. Fouvry and J. Klüners which proves that a conjecture provided by the Cohen–Lenstra philosophy implies another such conjecture. As a consequence of our work, we can deduce, for example, a conjecture for the probability laws of $p^j$-ranks of Selmer groups of elliptic curves. This is compatible with some theoretical works and other classical conjectures.


  • Christophe DelaunayUniversité de Franche-Comté
    Laboratoire de Mathématiques de Besançon
    CNRS UMR 6623
    Facultés des Sciences et Techniques
    16 route de Gray
    25030 Besançon, France
  • Frédéric JouhetUniversité de Lyon
    Université Lyon 1
    Institut Camille Jordan
    43, boulevard du 11 novembre 1918
    F-69622 Villeurbanne Cedex, France

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