The Rankin-Selberg method for automorphic distributions

We recently established the holomorphic continuation and functional equation of the exterior square L-function for GL(n,Z), and more generally, the archimedean theory of the GL(n) exterior square L-function over Q. We refer the reader to our paper [15] for a precise statement of the results and their relation to previous work on the subject. The purpose of this note is to give an account of our method in the simplest non-trivial cases, which can be explained without the technical overhead necessary for the general case. Let us begin by recalling the classical results, about standard L-functions and Rankin-Selberg L-functions of modular forms. We consider a cuspidal modular form F , of weight k, on the upper half plane H. To simplify the notation, we suppose that it is automorphic for Γ = SL(2,Z), though the arguments can be adapted to congruence subgroups of SL(2,Z). Like all modular forms, F has a Fourier expansion,