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On arithmetic statistics
Multi angle
Authors : Stevenhagen, Peter (Author of the conference)
CIRM (Publisher )
11K99 - None of the above but in this section
11R11 - Quadratic extensions
11R45 - Density theorems
CIRM (Publisher )
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Abstract :
We discuss Arithmetic Statistics as a 'new' branch of number theory by briefly sketching its development in the last 50 years. The non-triviality of the meaning of `random behaviour' and the problematic absence of good probability measures on countably infinite sets are illustrated by the example of the 1983 Cohen-Lenstra heuristics for imaginary quadratic class groups. We then focus on the Negative Pell equation, of which the random behaviour in the case of fundamental discriminants (Stevenhagen's conjecture) has now been established after 30 years.
We explain the open conjecture for the general case, which is based on equidistribution results for units over residue classes that remain to be proved.
Keywords : arithmetic statistics; negative Pell equation
MSC Codes : We explain the open conjecture for the general case, which is based on equidistribution results for units over residue classes that remain to be proved.
Keywords : arithmetic statistics; negative Pell equation
11K99 - None of the above but in this section
11R11 - Quadratic extensions
11R45 - Density theorems
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Information on the Video
Film maker : Petit, JeanLanguage : English Available date : 30/05/2023 Conference Date : 15/05/2023 Subseries : Research talks arXiv category : Number Theory 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/2023-05-15_Stevenhagen.mp4 
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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.20046303Cite this video as: Stevenhagen, Peter (2023). On arithmetic statistics. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20046303 URI : http://dx.doi.org/10.24350/CIRM.V.20046303 |
See Also
- [Multi angle] Integers expressible as the sum of two rational cubes / Author of the conference Bhargava, Manjul.
- [Multi angle] The average size of 3-torsion in class groups of 2-extensions / Author of the conference Matchett Wood, Melanie.
- [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
- STEVENHAGEN, Peter. The number of real quadratic fields having units of negative norm. Experimental Mathematics, 1993, vol. 2, no 2, p. 121-136. - https://doi.org/10.1080/10586458.1993.10504272
- STEVENHAGEN, Peter. Frobenius distributions for real quadratic orders. Journal de théorie des nombres de Bordeaux, 1995, vol. 7, no 1, p. 121-132. - https://jtnb.centre-mersenne.org/item/JTNB_1995__7_1_121_0/
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