Counting Maximal Arithmetic Subgroups

for absolute constants C6, C7. This theorem (almost) follows from [EV, Theorem 1.1], the only point being to control the dependence of implicit constants on the degree of the number field. We refer to [EV] for further information and for some motivational comments about the method. In the proof C1, C2, . . . will denote certain absolute constants. A.2. Let K be an extension of Q of degree d ≥ 200. Denote by Σ(K) the set of embeddings of K into C (#Σ(K) = d), and by Σ(K) a set of representatives for Σ(K) modulo complex conjugation (in the notations of the paper [EV] Σ(K) = V∞(K)). We regard the ring of integers OK as a lattice in K ⊗Q R = ∏