The aim of the present paper is to add, in several ways, to our understanding of the Cohen-Lenstra-Martinet heuristics on class groups of random number fields. Firstly, we point out several difficulties with the original formulation, and offer possible corrections. Secondly, we recast the heuristics in terms of Arakelov class groups of number fields. Thirdly, we propose a rigorously formulated Cohen-Lenstra-Martinet conjecture.

中文翻译：

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在随机数字段的班级组上

本文的目的是以几种方式增加我们对随机数字段类组的Cohen-Lenstra-Martinet启发式方法的理解。首先，我们指出了原始公式的几个困难，并提供了可能的更正。其次，我们根据数字字段的Arakelov类组来重试启发式方法。第三，我们提出了一个严格公式化的Cohen-Lenstra-Martinet猜想。