... of the r-th power of the class group of M, and assuch has cardinality εDr/2+εM/Q, by the easy part of the Brauer-Siegel theorem.On the other hand, the number of primes λ is |S|, and ... Substituting thesevalues of r, c into (2.6) yields the upper bound of Theorem 1.1.In the language of the beginning of this section, we have taken A tobe Spec RΣ and the map F to be FΣ. The set ... in terms of ∆L. There are onlyfinitely many such polynomials, and counting them gives the theorem of [18]. The main idea of Theorem 1.1 is to count r-tuples of integers in L instead of single...