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H 1 Towards ternary Goldbach's conjecture

Auteurs : Helfgott, Harald (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The ternary Goldbach conjecture (1742) asserts that every odd number greater than $5$ can be written as the sum of three prime numbers. Following the pioneering work of Hardy and Littlewood, Vinogradov proved (1937) that every odd number larger than a constant $C$ satisfies the conjecture. In the years since then, there has been a succession of results reducing $C$, but only to levels much too high for a verification by computer up to $C$ to be possible $(C>10^{1300})$. (Works by Ramare and Tao have solved the corresponding problems for six and five prime numbers instead of three.) My recent work proves the conjecture. We will go over the main ideas of the proof.
    ternary Goldbach conjecture - sums of primes - circle method

    Codes MSC :
    11N35 - Sieves
    11P32 - "Goldbach-type theorems; other additive questions involving primes"

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 28/05/2014
      Date de captation : 18/06/13
      Collection : Research talks ; Number Theory
      Format : quicktime ; audio/x-aac
      Durée : 00:57:11
      Domaine : Number Theory
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2013-06-18_Helfgott.mp4

    Informations sur la rencontre

    Nom de la rencontre : Analytic number theory / Théorie analytique des nombres
    Organisateurs de la rencontre : De la Bretèche, Régis ; Kowalski, Emmanuel ; Michel, Philippe ; Rivat, Joël
    Dates : 17/06/13 - 21/06/13
    Année de la rencontre : 2013
    URL Congrès : http://fouvry60.epfl.ch/

    Citation Data

    DOI : 10.24350/CIRM.V.18577403
    Cite this video as: Helfgott, Harald (2013). Towards ternary Goldbach's conjecture. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18577403
    URI : http://dx.doi.org/10.24350/CIRM.V.18577403


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