On class groups of random number fields

被引：6

作者：

Bartel, Alex ^{[1
]}

Lenstra, Hendrik W., Jr. ^{[2
]}

机构：

[1] Univ Glasgow, Sch Math & Stat, Univ Pl, Glasgow G12 8SQ, Lanark, Scotland

[2] Leiden Univ, Math Inst, Postbus 9512, NL-2300 RA Leiden, Netherlands

来源：

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2020年 / 121卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

11R23; 11R29; 60F99 (primary); DENSITY; EXTENSIONS; HEURISTICS;

D O I：

10.1112/plms.12343

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：927 / 953

页数：27

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