The $16$ -rank of $\mathbb{Q}(\sqrt{-p})$

preprint2019arXivOpen access

Recently, a density result for the $16$ -rank of $\text{Cl}(\mathbb{Q}(\sqrt{-p}))$ was established when $p$ varies among the prime numbers, assuming a short character sum conjecture. In this paper we prove the same density result unconditionally.

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The $16$ -rank of $\mathbb{Q}(\sqrt{-p})$

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The 161616-rank of Q(−p)\mathbb{Q}(\sqrt{-p})Q(−p​)

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The $16$ -rank of $\mathbb{Q}(\sqrt{-p})$