The \(GL(3)\) Rankin-Selberg convolution for functions not of rapid decay
The Rankin-Selberg method has been studied in great generality in a large number of cases when the automorphic forms involved are cuspidal, i.e. of rapid decay. Only in the case \(GL_ 2\) this method was worked out (independently) by Patterson and Zagier for functions which are not of rapid decay. In this paper this theme is taken up in the case \(GL_ 3\). It gives a result for the Rankin-Selberg convolution of a \(GL_ 3(\mathbb{C})\) noncuspidal automorphic form with the maximal parabolic \(GL_ 3(\mathbb{R})\) Eisenstein series. In this case, the proof that the convolution evaluates to the correct Dirichlet series is almost identical to the proof in the case of a cusp form. The main task left is to determine the analytic behavior of the convolution.
scientific article; zbMATH DE number 179237