The Rankin-Selberg method for automorphic distributions

Details The Rankin-Selberg method for automorphic distributions The Rankin-Selberg method for automorphic distributions

2006-05-31

arxiv.org/abs/math/0605783v1

Mathematics

Number Theory

38 pages, to appear in "Representation Theory and Automorphic Forms", Procedings of an International Symposium at Seoul Nation

Scientific paper

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).

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