Conference abstracts

Session A3 - Computational Number Theory - Semi-plenary talk

July 10, 15:30 ~ 16:20

3-ranks of cubic class groups

Peter Stevenhagen

Universiteit Leiden, Netherlands   -

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).

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FoCM 2017, based on a nodethirtythree design.