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

Djordjo Milovic

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arXiv · 1511.07127

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

Djordjo Milovic

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Abstract

We use a variant of Vinogradov's method to show that the density of the set of prime numbers $p\equiv -1\bmod~4$ 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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BibTeX RIS

Djordjo Milovic. 2017-06-11. On the $16$-rank of class groups of $\mathbb{Q}(\sqrt{-8p})$ for $p\equiv -1\bmod 4$. https://arxiv.org/abs/1511.07127

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