ON L-FUNCTIONS AND INTERTWINING-OPERATORS FOR UNITARY GROUPS

The ingredients of an "L-function machine" for the quasi-split group U(n,n + 1) X 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 local L 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.