ABSTRACT
Our purpose here is to present some results of the last decade lying in the intersection of modular forms, hyperbolic geometry and diophantine approximation to an audience primarily composed of the specialists in the latter area. As such, very basic facts in the two former areas will be touched upon, while much will be taken for granted in the area of diophantine approximation. This paper is the written expansion of an informal and leisurely talk; it will retain some of the informality of its precursor, but not, we trust, at the expense of clarity and correctness.
