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Large gaps between primes in subsets
Post-edited
Authors : Maynard, James (Author of the conference)
CIRM (Publisher )
11N05 - Distribution of primes
11N35 - Sieves
11N36 - Applications of sieve methods
CIRM (Publisher )
Abstract :
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.
MSC Codes : 11N05 - Distribution of primes
11N35 - Sieves
11N36 - Applications of sieve methods
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 01/06/17 Conference Date : 23/05/17 Series : The Fields Medallists Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:49:39 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-05-24_Maynard.mp4 
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Information on the Event
Event Title : Prime numbers and automatic sequences: determinism and randomness / Nombres premiers et suites automatiques : aléa et déterminismeEvent Organizers : Dartyge, Cécile ; Drmota, Michael ; Martin, Bruno ; Mauduit, Christian ; Rivat, Joël ; Stoll, Thomas Dates : 22/05/17 - 26/05/17 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1595.html
Citation Data
DOI : 10.24350/CIRM.V.19170903Cite 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 |
See Also
- [Multi angle] Bounded remainder sets for the discrete and continuous irrational rotation / Author of the conference Grepstad, Sigrid.
- [Multi angle] Large character sums / Author of the conference Lamzouri, Youness.
- [Multi angle] Small sumsets in continuous and discrete settings / Author of the conference de Roton, Anne.
- [Multi angle] Angles of Gaussian primes / Author of the conference Rudnick, Zeév.
Bibliography
- 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
