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H 1 Towards ternary Goldbach's conjecture

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

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 Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 28/05/2014 Date de captation : 18/06/13 Collection : Research talks Format : quicktime ; audio/x-aac Durée : 00:57:11 Domaine : Number Theory Audience : Chercheurs ; Doctorants , Post - Doctorants Download : http://videos.cirm-math.fr/2013-06-18_Helfgott.mp4 Informations sur la rencontre Nom du congrès : Analytic number theory / Théorie analytique des nombresOrganisteurs Congrès : De la Bretèche, Régis ; Kowalski, Emmanuel ; Michel, Philippe ; Rivat, JoëlDates : 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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