Two Applications of the Curve Lemma for Orthogonal Groups

Here H denotes the complex upper half plane and wτ the order of the stabilizer of τ in PSL2(Z). One purpose of this note is to give a generalization of this formula to modular forms on the orthogonal group O(2, p), which only depends on the Baily-Borel compactification of the arithmetic quotient in question. Moreover, we show that certain integrals, occurring in Arakelov intersection theory, associated with modular forms on O(2, p) converge.