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

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 $p\equiv 1\mathrm{mod}4$ is a prime.

16 pages

References in corpus (2)

• $2^{\infty }$-Selmer groups, $2^{\infty }$-class groups, and Goldfeld's conjecture
• Governing fields and statistics for 4-Selmer groups and 8-class groups

Cited by in corpus (3)

• The $16$-rank of $\mathbb{Q}(\sqrt{-p})$
• Elliptic curves and spin
• The $3$-isogeny Selmer groups of the elliptic curves $y^2=x^3+n^2$