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H 0 Automatic sequences along squares and primes

Auteurs : Drmota, Michael (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Automatic sequences and their number theoretic properties have been intensively studied during the last 20 or 30 years. Since automatic sequences are quite regular (they just have linear subword complexity) they are definitely no "quasi-random" sequences. However, the situation changes drastically when one uses proper subsequences, for example the subsequence along primes or squares. It is conjectured that the resulting sequences are normal sequences which could be already proved for the Thue-Morse sequence along the subsequence of squares.
    This kind of research is very challenging and was mainly motivated by the Gelfond problems for the sum-of-digits function. In particular during the last few years there was a spectacular progress due to the Fourier analytic method by Mauduit and Rivat. In this talk we survey some of these recent developments. In particular we present a new result on subsequences along primes of so-called invertible automatic sequences.

    11B85 - Automata sequences

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 20/10/14
      Date de captation : 12/02/14
      Collection : Research talks ; Number Theory
      Format : quicktime ; audio/x-aac
      Durée : 00:44:09
      Domaine : Number Theory
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2014-02-12_Drmota.mp4

    Informations sur la rencontre

    Nom de la rencontre : Prime numbers : new perspectives / Nombres premiers : nouvelles perspectives
    Organisateurs de la rencontre : Dartyge, Cécile ; Mauduit, Christian ; Rivat, Joël ; Stoll, Thomas
    Dates : 10/02/14 - 14/02/14
    Année de la rencontre : 2014

    Citation Data

    DOI : 10.24350/CIRM.V.18610403
    Cite this video as: Drmota, Michael (2014). Automatic sequences along squares and primes.CIRM . Audiovisual resource. doi:10.24350/CIRM.V.18610403
    URI : http://dx.doi.org/10.24350/CIRM.V.18610403