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Nonunique models in the Rankin-Selberg method. (English) Zbl 0833.11017
In the usual paradigm of the Rankin-Selberg method, a global integral exhibiting a functional equation unfolds to a unique model such as a Whittaker model, and consequently has an Euler product. Historically a few examples have been known in which the global integral unfolds to a non-unique model, but which nevertheless can be shown to represent an Euler product. In this paper new examples of this phenomenon are given, including the simplest know examples. For example, it is shown that if a cuspidal automorphic form on \(GL (2n)\) is restricted to \(GL(n)\) and integrated against \(\text{det} (g)^{s- 1/2}\), one obtains the standard \(L\)-function.
Reviewer: D.Bump (Stanford)

MSC:
11F66 Langlands \(L\)-functions; one variable Dirichlet series and functional equations
11F70 Representation-theoretic methods; automorphic representations over local and global fields
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