  This paper describes our method of pairing automorphic distributions. This
represents a third technique for obtaining the analytic properties of
automorphic L-functions, in addition to the existing methods of integral
representations (Rankin-Selberg) and Fourier coefficients of Eisenstein series
(Langlands-Shahidi). We recently used this technique to establish new cases of
the full analytic continuation of the exterior square L-functions. The paper
here gives an exposition of our method in two special, yet representative
cases: the Rankin-Selberg tensor product L-functions for PGL(2,Z), as well as
for the exterior square L-functions for GL (4,Z).
