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

Abstract

Let π be a cuspidal automorphic representation of GL₃($\Bbb A$$\Bbb Q$), unramified at p and of cohomological type at infinity. We construct p-adic L-functions, which interpolate the critical values of L(π,s) and which satisfy a logarithmic growth condition. We obtain these functions as p-adic Mellin transforms of certain distributions μ_π on $\Bbb Z$_p^* having values in some fixed number field and which are of moderate growth. In the p-ordinary case we obtain the bound |μ_π(U)|_p[les ]|μ_Haar(U)|_p for open subsets U[les ] $\Bbb Z$_p^*, where μ_Haar denotes the invariant distribution on $\Bbb Z$_p^*.