Session A3 - Computational Number Theory - Semi-plenary talk
July 10, 15:30 ~ 16:20
3-ranks of cubic class groups
Universiteit Leiden, Netherlands - email@example.com
A lot is known about the 2-part of class groups of quadratic number fields, with fundamental results as old as Gauss's description of the genera of binary quadratic forms, and of their ambiguous classes. Results for 4-ranks and 8-ranks of quadratic class groups were proved by Redei (1939), and his methods have been used to prove density results for quadratic discriminants with 2-class groups of prescribed behaviour, and even some cases of the largely unproved Cohen-Lenstra heuristics for class groups.
In this talk, we explore analogues of the quadratic results in the context of 3-parts of class groups of cubic number fields.
Joint work with Erick Knight (Max Planck Institut für Mathematik, Bonn) and Abtien Javanpeykar (Universiteit Leiden).