OnL-functions and intertwining operators for unitary groups

The ingredients of an “L-function machine” for the quasi-split groupU _{n, n} +1 × Res GL _n are treated here, following similar theories of P. Shapiro and S. Gelbart. We start with a known Rankin-Selberg type integral having an Euler product. In section 2 we compute the local integral to get a localL function. This is done by working with an “L group” related to ^L G and the relative root system. All computations are carried out for the split and the non-split case. In section 3 we address the problem of analytic continuation of the Eisenstein series. This involves computation of poles of intertwining operators.