On the $16$-rank of class groups of $\mathbb{Q}(\sqrt{-2p})$ for primes $p \equiv 1 \bmod 4$

Abstract

We use Vinogradov's method to prove equidistribution of a spin symbol governing the $16$-rank of class groups of quadratic number fields $\mathbb{Q}(\sqrt{-2p})$, where $p \equiv 1 \bmod 4$ is a prime.