Bartel, A. and Lenstra Jr., H. W. (2020) On class groups of random number fields. Proceedings of the London Mathematical Society, 121(4), pp. 927-953. (doi: 10.1112/plms.12343)
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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.
| Item Type: | Articles |
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| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Bartel, Professor Alex |
| Authors: | Bartel, A., and Lenstra Jr., H. W. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Proceedings of the London Mathematical Society |
| Publisher: | London Mathematical Society |
| ISSN: | 0024-6115 |
| ISSN (Online): | 1460-244X |
| Published Online: | 18 May 2020 |
| Copyright Holders: | Copyright © 2020 The Authors |
| First Published: | First published in Proceedings of the London Mathematical Society 121(4):927-953 |
| Publisher Policy: | Reproduced under a Creative Commons license |
| Related URLs: |
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