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H 1 Hilbert cubes in arithmetic sets

Auteurs : Elsholtz, Christian (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Let $S$ be a multiplicatively defined set. Ostmann conjectured, that the set of primes cannot be (nontrivially) written as a sumset $P\sim A+B$ (even in an asymptotic sense, when finitely many deviations are allowed). The author had previously proved that there is no such ternary sumset $P\sim A+B+C$ (with $ \left |A \right |,\left |B \right |,\left |C \right |\geq 2$). More generally, in recent work we showed (with A. Harper) for certain multiplicatively defined sets $S$, namely those which can be treated by sieves, or those with some equidistribution condition of Bombieri-Vinogradov type, that again there is no (nontrivial) ternary decomposition $P\sim A+B+C$. As this covers the case of smooth numbers, this settles a conjecture of A.Sárközy.
    Joint work with Adam J. Harper.

    05-XX - Combinatorics, {For finite fields, See 11Txx}
    11-XX - Number theory

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 13/10/14
      Date de captation : 03/02/14
      Collection : Research talks ; Combinatorics ; Number Theory
      Format : quicktime ; audio/x-aac
      Durée : 00:31:46
      Domaine : Combinatorics ; Number Theory
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2014-02-03_Elsholtz.mp4

    Informations sur la rencontre

    Nom de la rencontre : Jean-Morlet Chair - Main conference : unlikely intersections / Chaire Jean-Morlet - Conférence principale
    Organisateurs de la rencontre : Shparlinski, Igor
    Dates : 03/02/2014 - 07/02/14
    Année de la rencontre : 2014
    URL Congrès : https://www.chairejeanmorlet.com/1059a.html

    Citation Data

    DOI : 10.24350/CIRM.V.18607103
    Cite this video as: Elsholtz, Christian (2014). Hilbert cubes in arithmetic sets.CIRM . Audiovisual resource. doi:10.24350/CIRM.V.18607103
    URI : http://dx.doi.org/10.24350/CIRM.V.18607103



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