Let K be a cyclic, totally real extension of Q of degree at least
3, and let σ be a generator of Gal(K/Q).
We further assume that the totally positive units are exactly the squares of units. In this case, Friedlander,
Iwaniec, Mazur and Rubin define the spin of an odd principal ideal a to be spin(σ, a) = (α/σ(a))K, where
α is a totally positive generator of a and (*/*) is the quadratic residue symbol in K. Friedlander, Iwaniec,
Mazur and Rubin prove equidistribution of spin(σ, p) as p varies over the odd principal prime ideals of K.
In this talk I will show how to extend their work to more general fields. I will then give various arithmetic
This is a joint work with Djordjo Milovic.