Jean-Morlet Chair - Conference - Arithmetic Statistics / Chaire Jean-Morlet - Conférence - Statistiques arithmétiques

Collection Jean-Morlet Chair - Conference - Arithmetic Statistics / Chaire Jean-Morlet - Conférence - Statistiques arithmétiques

Organisateur(s) Anni, Samuele ; Lorenzo Garcia, Elisa ; Stevenhagen, Peter ; Vonk, Jan

Date(s) 15/05/2023 - 19/05/2023

URL associée https://conferences.cirm-math.fr/2675.html

00:00:00 / 00:00:00

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On arithmetic statistics

De Peter Stevenhagen

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.

Informations sur la vidéo

Date de captation 15/05/2023
Date de publication 30/05/2023
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Jean Petit
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20046303
Citer cette vidéo Stevenhagen, Peter (15/05/2023). On arithmetic statistics. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20046303
URL https://dx.doi.org/10.24350/CIRM.V.20046303

Domaine(s)

Théorie des nombres

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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