English
On arithmetic statistics
Multi angle
Auteurs : Stevenhagen, Peter (Auteur de la Conférence)
CIRM (Editeur )
11K99 - None of the above but in this section
11R11 - Quadratic extensions
11R45 - Density theorems
CIRM (Editeur )
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Résumé :
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
Codes MSC : 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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Informations sur la Vidéo
Réalisateur : Petit, JeanLangue : Anglais Date de publication : 30/05/2023 Date de captation : 15/05/2023 Sous collection : Research talks arXiv category : Number Theory Domaine : Number Theory Format : MP4 (.mp4) - HD Durée : 01:07:10 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-05-15_Stevenhagen.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair - Conference - Arithmetic Statistics / Chaire Jean-Morlet - Conférence - Statistiques arithmétiquesOrganisateurs de la rencontre : Anni, Samuele ; Lorenzo Garcia, Elisa ; Stevenhagen, Peter ; Vonk, Jan Dates : 15/05/2023 - 19/05/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2675.html
Données de citation
DOI : 10.24350/CIRM.V.20046303Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] Integers expressible as the sum of two rational cubes / Auteur de la Conférence Bhargava, Manjul.
- [Multi angle] The average size of 3-torsion in class groups of 2-extensions / Auteur de la Conférence Matchett Wood, Melanie.
- [Multi angle] Quadratic twist families of elliptic curves with unusual $2^{\infty }$-Selmer groups / Auteur de la Conférence Smith, Alexander.
- [Multi angle] Subrings of number fields / Auteur de la Conférence Lenstra, Hendrik.
- [Multi angle] Vanishing of twisted L-functions of elliptic curves over function fields / Auteur de la Conférence Lalin, Matilde.
Bibliographie
- 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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