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On the $16$-rank of class groups of $\mathbb{Q}(\sqrt{-p})$. (arXiv:1611.10337v2 [math.NT] UPDATED)

来源于:arXiv
Let $p$ be a prime number and let $\mathrm{Cl}_{\mathbb{Q}(\sqrt{-p})}$ denote the class group of the imaginary quadratic number field $\mathbb{Q}(\sqrt{-p})$. We use Vinogradov's method to show that a spin symbol governing the $16$-rank of $\mathrm{Cl}_{\mathbb{Q}(\sqrt{-p})}$ is equidistributed, conditional on a standard conjecture about short character sums. This proves that the density of the set of prime numbers $p$ for which $\mathrm{Cl}_{\mathbb{Q}(\sqrt{-p})}$ has an element of order $16$ is equal to $\frac{1}{16}$. 查看全文>>