Rankin-Selberg Integrals and L-Functions for Covering Groups of General Linear Groups

Let GL(m)c be the covering group of GLc, obtained by restriction from the m-fold central extension of Matsumoto of the symplectic group. We introduce a new family of Rankin- Selberg integrals for representations of GL(m)c × GL(m)k. The construction is based on certain assumptions, which we prove here for k = 1. Using the integrals, we define local γ -, L-, and ∈-factors. Globally, our construction is strong in the sense that the integrals are truly Eulerian. This enables us to define the completed L-function for cuspidal representations and prove its standard functional equation.