On class groups of random number fields
Number Theory
2020-06-16 v4
Abstract
The main aim of the present paper is to disprove the Cohen--Lenstra--Martinet heuristics in two different ways and to offer possible corrections. We also recast the heuristics in terms of Arakelov class groups, giving an explanation for the probability weights appearing in the general form of the heuristics. We conclude by proposing a rigorously formulated Cohen--Lenstra--Martinet conjecture.
Keywords
Cite
@article{arxiv.1803.06903,
title = {On class groups of random number fields},
author = {Alex Bartel and Hendrik W. Lenstra},
journal= {arXiv preprint arXiv:1803.06903},
year = {2020}
}
Comments
Expanded introduction, and other minor improvements in the exposition, 31 pages. Final version, to appear in Proc. London Math. Soc