ORDINARY p-ADIC EISENSTEIN SERIES AND p-ADIC L-FUNCTIONS FOR UNITARY GROUPS

The purpose of this work is to carry out the first step in our four-step program towards the main conjecture for GL(2) x K-x by the method of Eisenstein congruence on GU(3, 1), where K is an imaginary quadratic field. We construct a p-adic family of ordinary Eisenstein series on the group of unitary similitudes GU (3, 1) with the optimal constant term which is basically the product of the Kubota-Leopodlt p-adic L-function and a p-adic L-function for GL(2) x K-x. This construction also provides a different point of view of p-adic L-functions of GL(2) x K-x.