The Full Version of Theorem 1.3

Abstract

We use the same setup as in the previous chapter: L/E is a quadratic extension of totally real fields ${\rm Gal}{(L/E)}={\langle 1,\varsigma\rangle},\,{\rm Gal}{(L/E)}^\wedge={\langle 1,\eta\rangle},\mathfrak{c}\subset\mathcal{O}_L$ is an ideal, and

$$n:=[L:\mathbb{Q}], \quad d:=d_{L/E},\quad \mathcal {D}:=\mathcal{D}_{L/E},\quad\mathfrak{c}_{E}:=\mathfrak{c}\cap\mathcal{O}_E.$$