English
Large gaps between primes in subsets
Post-edited
Auteurs : Maynard, James (Auteur de la conférence)
CIRM (Editeur )
11N05 - Distribution of primes
11N35 - Sieves
11N36 - Applications of sieve methods
CIRM (Editeur )
Résumé :
All previous methods of showing the existence of large gaps between primes have relied on the fact that smooth numbers are unusually sparse. This feature of the argument does not seem to generalise to showing large gaps between primes in subsets, such as values of a polynomial. We will talk about recent work which allows us to show large gaps between primes without relying on smooth number estimates. This then generalizes naturally to show long strings of consecutive composite values of a polynomial. This is joint work with Ford, Konyagin, Pomerance and Tao.
Codes MSC : 11N05 - Distribution of primes
11N35 - Sieves
11N36 - Applications of sieve methods
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 01/06/17 Date de Captation : 23/05/17 Collection : The Fields Medallists Sous Collection : Research talks Catégorie arXiv : Number Theory Domaine(s) : Théorie des Nombres Format : MP4 (.mp4) - HD Durée : 00:49:39 Audience : Chercheurs Download : https://videos.cirm-math.fr/2017-05-24_Maynard.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Prime numbers and automatic sequences: determinism and randomness / Nombres premiers et suites automatiques : aléa et déterminismeOrganisateurs de la Rencontre : Dartyge, Cécile ; Drmota, Michael ; Martin, Bruno ; Mauduit, Christian ; Rivat, Joël ; Stoll, Thomas Dates : 22/05/17 - 26/05/17 Année de la rencontre : 2017 URL de la Rencontre : http://conferences.cirm-math.fr/1595.html
Données de citation
DOI : 10.24350/CIRM.V.19170903Citer cette vidéo: Maynard, James (2017). Large gaps between primes in subsets. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19170903 URI : http://dx.doi.org/10.24350/CIRM.V.19170903 |
Voir Aussi
- [Multi angle] Bounded remainder sets for the discrete and continuous irrational rotation / Auteur de la conférence Grepstad, Sigrid.
- [Multi angle] Large character sums / Auteur de la conférence Lamzouri, Youness.
- [Multi angle] Small sumsets in continuous and discrete settings / Auteur de la conférence de Roton, Anne.
- [Multi angle] Angles of Gaussian primes / Auteur de la conférence Rudnick, Zeév.
Bibliographie
- Ford, K., Green, B., Konyagin, S., & Tao, S. (2015). Large gaps between consecutive prime numbers.
- Maynard, J. (2016). Large gaps between primes. Annals of Mathematics. Second Series, 183(3), 915-933 - http://dx.doi.org/10.4007/annals.2016.183.3.3
- Rankin, R.A. (1938). The difference between consecutive prime numbers. I. Journal of the London Mathematical Society, 13, 242-247 - http://dx.doi.org/10.1112/jlms/s1-13.4.242
