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Primes in arithmetic progressions and bounded gaps
Multi angle
Authors : Stadlmann, Julia (Author of the conference)
CIRM (Publisher )
11L07 - Estimates on exponential sums
11N05 - Distribution of primes
11N36 - Applications of sieve methods
Additional resources :
https://www.cirm-math.fr/RepOrga/3213/Slides/Harper-slides.pdf
CIRM (Publisher )
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Abstract :
Following Zhang's breakthrough on bounded gaps between primes, much work has gone into improving upper bounds on the smallest integer which appears infinitely often as the gap between a given number of primes. Equidistribution estimates for primes in certain arithmetic progressions are a key ingredient of Zhang's proof and later work of Polymath. In this talk, I will highlight how bounded gaps and primes in arithmetic progressions are linked, and I will discuss obstacles and recent successes in using various types of old and new equistribution estimates to improve on the results of Polymath for bounded gaps between primes.
Keywords : gaps between primes; GPY method; equidistribution estimates; arithmetic progressions
MSC Codes : Keywords : gaps between primes; GPY method; equidistribution estimates; arithmetic progressions
11L07 - Estimates on exponential sums
11N05 - Distribution of primes
11N36 - Applications of sieve methods
Additional resources :
https://www.cirm-math.fr/RepOrga/3213/Slides/Harper-slides.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/07/2025 Conference Date : 23/06/2025 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:26:56 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-06-23_Stadlmann.mp4 
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Information on the Event
Event Title : Prime numbers and arithmetic randomness / Nombres premiers et aléa arithmétiqueEvent Organizers : Elsholtz, Christian ; Ostafe, Alina ; Rivat, Joël ; Stoll, Thomas ; Swaenepoel, Cathy Dates : 23/06/2025 - 27/06/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3213.html
Citation Data
DOI : 10.24350/CIRM.V.20368603Cite this video as: Stadlmann, Julia (2025). Primes in arithmetic progressions and bounded gaps. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20368603 URI : http://dx.doi.org/10.24350/CIRM.V.20368603 |
See Also
- [Multi angle] Recent progress on some irrationality questions of Erdős / Author of the conference Pratt, Kyle.
- [Multi angle] Improved bounds for the Fourier uniformity conjecture / Author of the conference Pilatte, Cédric.
- [Multi angle] A two dimensional delta symbol method and applications / Author of the conference Li, Junxian.
- [Multi angle] Sums of odd-ly many fractions and the distribution of primes / Author of the conference Kuperberg, Vivian.
Bibliography
- BAKER, R. C. et IRVING, A. J. Bounded intervals containing many primes. Mathematische Zeitschrift, 2017, vol. 286, p. 821-841. - https://doi.org/10.1007/s00209-016-1786-7
- GOLDSTON, Daniel A., PINTZ, János, et YILDIRIM, Cem Y. Primes in tuples I. Annals of Mathematics, 2009, p. 819-862. - https://doi.org/10.4007/annals.2009.170.819
- MAYNARD, James. Small gaps between primes. Annals of mathematics, 2015, p. 383-413. - https://doi.org/10.4007/annals.2015.181.1.7
- POLYMATH, D. H. J. New equidistribution estimates of Zhang type. Algebra & Number Theory, 2014, vol. 8, no 9, p. 2067-2199. - http://dx.doi.org/10.2140/ant.2014.8.2067
- POLYMATH, D. H. J. Variants of the Selberg sieve, and bounded intervals containing many primes. Research in the Mathematical sciences, 2014, vol. 1, p. 1-83. - http://dx.doi.org/10.1186/s40687-015-0033-x
- STADLMANN, Julia. On primes in arithmetic progressions and bounded gaps between many primes. Advances in Mathematics, 2025, vol. 468, p. 110190. - https://doi.org/10.1016/j.aim.2025.110190
- ZHANG, Yitang. Bounded gaps between primes. Annals of Mathematics, 2014, p. 1121-1174. - https://doi.org/10.4007/annals.2014.179.3.7
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