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On the 16-rank of class groups of \({\mathbb{Q}(\sqrt{-8p})}\) for \({p \equiv -1 {\rm mod} 4}\)

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Abstract

We use a variant of Vinogradov’s method to show that the density of the set of prime numbers \({p \equiv -1 {\rm mod} 4}\) for which the class group of the imaginary quadratic number field \({\mathbb{Q}(\sqrt{-8p})}\) has an element of order 16 is equal to 1/16, as predicted by the Cohen–Lenstra heuristics.

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  1. School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ, 08540, USA

    Djordjo Milovic

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Milovic, D. On the 16-rank of class groups of \({\mathbb{Q}(\sqrt{-8p})}\) for \({p \equiv -1 {\rm mod} 4}\) . Geom. Funct. Anal. 27, 973–1016 (2017). https://doi.org/10.1007/s00039-017-0419-6

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