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Post-edited Large gaps between primes in subsets

Auteurs : Maynard, James (Auteur de la Conférence)
CIRM (Editeur )

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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

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 01/06/17
    Date de captation : 23/05/17
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 00:49:39
    Domaine : Number Theory
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : http://videos.cirm-math.fr/2017-05-24_Maynard.mp4

Informations sur la rencontre

Nom du congrès : Prime numbers and automatic sequences: determinism and randomness / Nombres premiers et suites automatiques : aléa et déterminisme
Organisteurs Congrès : 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 Congrès : http://conferences.cirm-math.fr/1595.html

Citation Data

DOI : 10.24350/CIRM.V.19170903
Cite this video as: 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

Bibliographie

  1. Ford, K., Green, B., Konyagin, S., & Tao, S. (2015). Large gaps between consecutive prime numbers. <arXiv:1408.4505> - https://arxiv.org/abs/1408.4505

  2. 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

  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



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