A Rankin-Selberg integral for the adjoint representation of GL3
Copyright policy )A Rankin-Selberg integral for the adjoint representation of GL3
This paper deals with some problems towards the analytic continuation and functional equation of the \(L\)-function \(L(s,\pi,r)\) attached to a cuspidal representation of \(GL_ 3\) and the eight dimensional adjoint representation \(r\) of the \(L\)-group \(GL_ 3(\mathbb{C})\) of \(GL_ 3\). The Basic Identity is established for the global zeta-integral; the latter one is shown to be Eulerian with Whittaker model. Then the unramified local zeta-integrals are compared with the Langlands factors. In all this basic use is made of the embedding of \(SL_ 3\) into \(G_ 2\).
- DigiZeitschriften Germany
- Yale University United States
Zeta functions and \(L\)-functions, Euler product with Whittaker model, cuspidal representation, Article, unramified local zeta- integrals, automorphic L-functions, analytic continuation, 510.mathematics, Representation-theoretic methods; automorphic representations over local and global fields, Langlands \(L\)-functions; one variable Dirichlet series and functional equations, Zeta functions and \(L\)-functions of number fields, functional equation, Rankin-Selberg integral, global zeta-integral
Zeta functions and \(L\)-functions, Euler product with Whittaker model, cuspidal representation, Article, unramified local zeta- integrals, automorphic L-functions, analytic continuation, 510.mathematics, Representation-theoretic methods; automorphic representations over local and global fields, Langlands \(L\)-functions; one variable Dirichlet series and functional equations, Zeta functions and \(L\)-functions of number fields, functional equation, Rankin-Selberg integral, global zeta-integral
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