Statistics of ray class groups of quadratic number fields

Alex Bartel (U of Glasgow)

Sep 24. 2021, 09:15 — 10:15

Varma computed the average size of 3-torsion in ray class groups of quadratic fields with respect to a fixed modulus. In joint work with Carlo Pagano we formulate a heuristic that explains the numbers obtained by Varma by modelling these ray class groups as "random". However, the heuristics are much cleaner when phrased in terms of an object that, to our knowledge, has not been considered in the literature, and that we call the Arakelov ray class group of a number field. By taking the modulus to be trivial, one recovers the Cohen--Lenstra heuristics on class groups. I will explain all of this. See Carlo's talk for some partial results in support of our heuristic.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Arithmetic Statistics and Local-Global Principles (Workshop)
Tim Browning (ISTA, Klosterneuburg)
Daniel Loughran (U Bath)
Rachel Newton (KCL, London)