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arXiv · 1803.06903

On class groups of random number fields

Alex Bartel·Hendrik W. Lenstra Jr
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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.

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Alex Bartel, Hendrik W. Lenstra Jr. 2018-03-19. On class groups of random number fields. https://doi.org/10.1112/plms.12343

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