On class groups of random number fields

Proceedings of the London Mathematical Society, vol. 121, pp. 927–953

Abstract

The main aim of this 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.

Authors 1

1. Alex Bartel

   University of Glasgow

   Affiliation as printed

   School of Mathematics and Statistics University of Glasgow University Place Glasgow G12 8SQ United Kingdom