Français
Integers expressible as the sum of two rational cubes
Multi angle
Authors : Bhargava, Manjul (Author of the conference)
CIRM (Publisher )
11D25 - Cubic and quartic equations
11G05 - Elliptic curves over global fields
14G05 - Rational points
CIRM (Publisher )
Loading the player...
|
Abstract :
We prove that a positive proportion of integers can be expressed as a sum of two rational cubes, and a positive proportion can not. This is joint work with Levent Alpoge and Ari Shnidman.
MSC Codes : 11D25 - Cubic and quartic equations
11G05 - Elliptic curves over global fields
14G05 - Rational points
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 30/05/2023 Conference Date : 18/05/2023 Series : The Fields Medallists Subseries : Research talks arXiv category : Number Theory ; Algebraic Geometry Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 01:07:10 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-05-18-Bhargava.mp4 
|
Information on the Event
Event Title : Jean-Morlet Chair - Conference - Arithmetic Statistics / Chaire Jean-Morlet - Conférence - Statistiques arithmétiquesEvent Organizers : Anni, Samuele ; Lorenzo Garcia, Elisa ; Stevenhagen, Peter ; Vonk, Jan Dates : 15/05/2023 - 19/05/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2675.html
Citation Data
DOI : 10.24350/CIRM.V.20049303Cite this video as: Bhargava, Manjul (2023). Integers expressible as the sum of two rational cubes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20049303 URI : http://dx.doi.org/10.24350/CIRM.V.20049303 |
See Also
- [Multi angle] The average size of 3-torsion in class groups of 2-extensions / Author of the conference Matchett Wood, Melanie.
- [Multi angle] On arithmetic statistics / Author of the conference Stevenhagen, Peter.
- [Multi angle] Quadratic twist families of elliptic curves with unusual $2^{\infty }$-Selmer groups / Author of the conference Smith, Alexander.
- [Multi angle] Subrings of number fields / Author of the conference Lenstra, Hendrik.
- [Multi angle] Vanishing of twisted L-functions of elliptic curves over function fields / Author of the conference Lalin, Matilde.
Bibliography
- ALPÖGE, Levent, BHARGAVA, Manjul, et SHNIDMAN, Ari. Integers expressible as the sum of two rational cubes. arXiv preprint arXiv:2210.10730, 2022. - https://doi.org/10.48550/arXiv.2210.10730
