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Séminaire de Théorie Algorithmique des Nombres

Responsables : Xavier Caruso et Aurel Page

Page du séminaire

  • Le 22 juin 2021 à 10:00
  • Online
    Vandita Patel (University of Manchester)
    Shifted powers in Lucas-Lehmer sequences

    The explicit determination of perfect powers in (shifted) non-degenerate, integer, binary linear recurrence sequences has only been achieved in a handful of cases. In this talk, we combine bounds for linear forms in logarithms with results from the modularity of elliptic curves defined over totally real fields to explicitly determine all shifted powers by two in the Fibonacci sequence. A major obstacle that is overcome in this work is that the Hilbert newspace which we are interested in has dimension 6144. We will focus on how this space is computationally handled with respect to the underlying Diophantine equation. This is joint work with Mike Bennett (UBC) and Samir Siksek (Warwick).


  • Le 29 juin 2021 à 10:00
  • Online
    Pierre Briaud (Inria Paris)
    TBA

    TBA


  • Le 6 juillet 2021 à 10:00
  • Online
    Anna Somoza (IRMAR, Université de Rennes 1)
    TBA

    TBA


  • Le 14 septembre 2021 à 10:00
  • Online
    Benjamin Wesolowski (CNRS, IMB)
    TBA

    TBA


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