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

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.

References in corpus (5)

• On the mean number of 2-torsion elements in the class groups, narrow class groups, and ideal groups of cubic orders and fields
• $2^{\infty }$-Selmer groups, $2^{\infty }$-class groups, and Goldfeld's conjecture
• Nonabelian Cohen-Lenstra Moments
• The distribution of $H_8$-extensions of quadratic fields
• Statistics of $K$-groups modulo $p$ for the ring of integers of a varying quadratic number field

Cited by in corpus (1)

• A program to test the p-rationality of any number field