On the Asymptotics of a Prime Spin Relation II

Abstract

For K a cyclic cubic number field with odd class number containing a unit w such that Norm(w)=Norm(1-w)=-1, we prove that the density of rational primes p that satisfy the given spin relation is equal to 1/2. Furthermore, we prove that this density restricted to rational primes that are 1 mod 4 is 1/4 and this density restricted to rational primes that are -1 mod 4 is 3/4.

This November 2018 article contains limited content and will not be published. These results and an improvement on these results are included in another paper, "A Density of Ramified Primes" arXiv:2005.10188 by Stephanie Chan, Christine McMeekin, and Djordjo Milovic