Eisenstein Cohomology and the Construction of p-Adic Analytic L-Functions

Let be a cuspidal automorphic representation of GL₃(), unramified at pand of cohomological type at infinity. We construct p-adic L-functions, which interpolate the critical values of L(,s) and which satisfy a logarithmic growth condition. We obtain these functions as p-adic Mellin transforms of certain distributions on _p^*having values in some fixed number field and which are of moderate growth. In the p-ordinary case we obtain the bound |(U)|_p|_Haar(U)|_pfor open subsets U _p^*, where _Haardenotes the invariant distribution on _p^*.