Mathematical Sciences: Higher Regulators, Algebraic Cycles, and Values of L-functions

本研究将继续探讨循环结构的P.I.和算术变分的k理论及其与积分点上l -函数值的（推测）关系。他将分析Beilinson， Bloch和Tate在模变体的背景下的某些选定的猜想，其中可以使用自同构形式理论。这项研究是在融合主题包括数论，代数几何和自同构形式。也就是说，它运用代数、分析和几何的工具来分析数论问题。“l函数的值”给出了具有重要算术意义的显式数的解析表达式，以便对它们进行更深入的研究。在过去的研究中，P.I.对这一领域做出了许多有益的贡献，在今后的研究中也必将做出更大的贡献。

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.