Eisenstein cohomology and the construction of p-adic analytic L-functions

Let pi be a cuspidal automorphic representation of GL(3)(A(Q)), unramified at p and of cohomological type at infinity. We construct p-adic L-functions, which interpolate the critical values of L(pi, s) and which satisfy a logarithmic growth condition. We obtain these functions as p-adic Mellin transforms of certain distributions mu (pi) on Z(p)* having values in some fixed number field and which are of moderate growth. In the p-ordinary case we obtain the bound \mu (pi)(U)\(p) less than or equal to \mu (Haar)(U)\(p) for open subsets U less than or equal to Z(p)*, where mu (Haar) denotes the invariant distribution on Z(p)*.