This research will continue the investigations of the P.I. on the structure of cycles and K-theory of arithmetic varieties and their (conjectural) relationship to values of L-functions at integral points. He will analyze certain selected conjectures of Beilinson, Bloch and Tate in the context of modular varieties where one can use the theory of automorphic forms. This research is in the blend of topics encompassing number theory, algebraic geometry and automorphic forms. That is, it brings to bear tools from algebra, analysis and geometry to analyze number theoretic problems. The "values of L-functions" give analytic expression to explicit numbers of great arithmetic significance allowing for their deeper study. The P.I. has contributed many interests results to this area in the past and will surely do so further during this research.
