This research will concentrate on an investigation of integral representations of Dirichlet series, L-functions, automorphic forms and related objects. The kernels of interest for the integral representations are Eisenstein series on reductive algebraic groups or some suitable "fragments" of such Eisenstein series. Results on the nature of special values, analytic continuations and functional equations would follow from the existence of such integral representations. This research will focus on various analytic functions that encode important number theoretic information. This technique allows one to apply the deep results of analysis to obtain number theoretic information. A basic analytic tool is to represent these functions as integrals of functions which are better understood. That is precisely what the P.I. intends to do and has done so successfully in the past.
