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Recent progress on some irrationality questions of Erdős
Multi angle
Authors : Pratt, Kyle (Author of the conference)
CIRM (Publisher )
11J72 - "Irrationality; linear independence over a field"
11L03 - Trigonometric and exponential sums, general
11N05 - Distribution of primes
Additional resources :
https://www.cirm-math.fr/RepOrga/3213/Slides/Pratt_Erdos_irrationality.pdf
CIRM (Publisher )
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Abstract :
Paul Erdos posed many interesting problems on the irrationality of various infinite series. We give some history and motivation for these problems. We then describe some of our recent work (conditional and unconditional) on these irrationality questions, and the tools from prime number theory we have used.
Keywords : irrationality, sieves; prime numbers
MSC Codes : Keywords : irrationality, sieves; prime numbers
11J72 - "Irrationality; linear independence over a field"
11L03 - Trigonometric and exponential sums, general
11N05 - Distribution of primes
Additional resources :
https://www.cirm-math.fr/RepOrga/3213/Slides/Pratt_Erdos_irrationality.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/07/2025 Conference Date : 26/06/2025 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:33:37 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-06-26_Pratt.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.20368403Cite this video as: Pratt, Kyle (2025). Recent progress on some irrationality questions of Erdős. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20368403 URI : http://dx.doi.org/10.24350/CIRM.V.20368403 |
See Also
- [Multi angle] Primes in arithmetic progressions and bounded gaps / Author of the conference Stadlmann, Julia.
- [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
- PRATT, Kyle. The irrationality of a divisor function series of Erdös and Kac. Acta Arith. 211 (2023), no. 3, 193–228. - http://doi.org/10.4064/aa220927-1-9
- PRATT, Kyle. The irrationality of an infinite series involving ω (n) under a prime tuples conjecture. Journal of Number Theory, 2025. - https://doi.org/10.1016/j.jnt.2025.02.010
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