## The Rankin-Selberg method for automorphic distributions.(English)Zbl 1302.11033

Kobayashi, Toshiyuki (ed.) et al., Representation theory and automorphic forms. Based on the symposium, Seoul, Korea, February 14–17, 2005. Basel: Birkhäuser (ISBN 978-0-8176-4505-2/hbk). Progress in Mathematics 255, 111-150 (2008).
Summary: This paper describes our method of pairing automorphic distributions.We present 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 $$\mathrm{PGL}\setminus \mathrm{PGL}(2,\mathbb R)$$, as well as for the exterior square $$L$$-functions for $$\mathrm{GL}(4,\mathbb Z)\setminus \mathrm{GL}(4,\mathbb R)$$.
For the entire collection see [Zbl 1124.11004].

### MSC:

 11F70 Representation-theoretic methods; automorphic representations over local and global fields 11F66 Langlands $$L$$-functions; one variable Dirichlet series and functional equations 22E30 Analysis on real and complex Lie groups
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