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4-ranks and the general model for statistics of ray class groups of imaginary quadratic number fields

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arxiv 1710.07587 v1 pith:RMOMQWYK submitted 2017-10-20 math.NT

Carlo Pagano , Efthymios Sofos This is my paper · ORCID
classification math.NT
keywords classfieldsgroupsimaginarynumberquadraticranksasymptotically
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abstract

We extend the Cohen-Lenstra heuristics to the setting of ray class groups of imaginary quadratic number fields, viewed as exact sequences of Galois modules. By asymptotically estimating the mixed moments governing the distribution of a cohomology map, we prove these conjectures in the case of $4$-ranks.

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  1. Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields

    math.NT 2026-08 conditional novelty 8.0 of 10

    The 4-ranks of the class groups of Q(sqrt(-d)) and Q(sqrt(-d0 d)) are asymptotically independent, each with the Cohen-Lenstra-Gerth distribution.

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