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Mathematics > Number Theory

Title: On class groups of random number fields

Abstract: 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.
Comments: 28 pages; comments welcome!
Subjects: Number Theory (math.NT)
MSC classes: 11R29, 11R23, 60F99
Cite as: arXiv:1803.06903 [math.NT]
  (or arXiv:1803.06903v1 [math.NT] for this version)

Submission history

From: Alex Bartel [view email]
[v1] Mon, 19 Mar 2018 13:23:57 GMT (34kb)