Ari Shnidman (Hebrew University/IAS)
Event Date
2025-04-11
Event Time
02:30 pm ~ 03:30 pm
Event Location
Wachman Hall 617
Abstract: Heuristics of Cohen, Lenstra, Martinet, Malle and others predict the distribution of the p-part of the class group in families of number fields with prescribed degree and Galois group G, at least when p does not divide the order of G. Results in this direction are few and far between, most notably the results of Davenport--Heilbronn and Bhargava. We give a new data point by computing the average size of the 2-torsion in the class group of the cubic fields Q(n^{1/3}). Along the way, we prove a "reciprocity law" for 2-torsion ideal classes in general cubic fields, which indicates how the existing heuristics should be adjusted when p = 2. This is joint work with Artane Siad.