Let $F$ be a non-Archimedean locally compact field‎. ‎Let $sigma$ and $tau$ be finite-dimensional representations of the Weil-Deligne group of $F$‎. ‎We give strong upper and lower bounds for the Artin and Swan exponents of $sigmaotimestau$ in terms of those of $sigma$ and $tau$‎. ‎We give a different lower bound in terms of $sigmaotimeschecksigma$ and $tauotimeschecktau$‎. ‎Using the Langlands...

We describe two new Eulerian Rankin-Selberg integrals, using the same Eisenstein series defined on the group E8, and cuspidal representations from GL5 and GSpin11, respectively. Connections with past work of Ginzburg, Bump-Ginzburg, Jiang-Rallis and others are described. We give some details of how to relate our two integrals via formal manipulations. It is a fact of classical invariant theory ...

In this article we prove that given a holomorphic cusp form f and any point s0 in the complex plane, there is a holomorphic cusp form g such that the Rankin-Selberg L-function L(s, f × g) is non-zero at s0. Résumé: Dans cet article, on prouve le résultat suivant. Etat donné une forme holomorphe cuspidale f et un point quelquonque du plan complexe, il existe une forme holomorphe cuspidale g tell...