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# Single angle

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Single angle Hilbert cubes in arithmetic sets

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

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 Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 13/10/14 Date de captation : 03/02/14 Collection : Research talks Format : quicktime ; audio/x-aac Durée : 00:31:46 Domaine : Combinatorics ; Number Theory Audience : Chercheurs ; Doctorants , Post - Doctorants Download : http://videos.cirm-math.fr/2014-02-03_Elsholtz.mp4 Informations sur la rencontre Nom du congrès : Jean-Morlet Chair - Main conference : unlikely intersections / Chaire Jean-Morlet - Conférence principaleOrganisteurs Congrès : Shparlinski, IgorDates : 03/02/14 - 07/02/14 Année de la rencontre : 2014 URL Congrès : http://shparlinskikohel.weebly.com/infor... Citation DataDOI : 10.24350/CIRM.V.18607103Cite this video as: Elsholtz, Christian (2014). Hilbert cubes in arithmetic sets.CIRM . Audiovisual resource. doi:10.24350/CIRM.V.18607103URI : http://dx.doi.org/10.24350/CIRM.V.18607103

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