Mathematical Sciences: Plancherel Measures and Automorphic L-Functions

本研究涉及以下领域的研究： 表示理论和自守形式。 首先是 研究了p-空间定义调和L-包的可能性， 利用某个映射的对偶的进约化群 来自轨道积分的转移。 存在这种 地图，即使还没有证明一般是现在相当 是稳定微量公式的基础 关于Langlands 第二个问题涉及R-群的理论 对于从非离散回火 一个p-adic群的表示。 主要研究者 他还将致力于统一不同的方法， 学习自守L函数 最后，他将努力扩大 他关于某些自守L- 他们中的一个更大的类的功能。 算术函数的生成函数是众所周知的 和强大的工具来研究这些功能。 最深的 在所有这些研究中，最博学的是所谓的朗格兰的 程序. 但这个项目的好处是非常高的。 这 研究在这个领域。

This research concerns the study of the following areas of representation theory and automorphic forms. The first is the study of the possibility of defining tempered L-packets for p- adic reductive groups by means of the dual of a certain map coming from transfer of orbital integrals. The existence of this map even though not yet proved in general is by now fairly accepted and is the basis of stabilization of the trace formula by Langlands. The second problem concerns the theory of R-groups for representations induced from non-discrete tempered representations of a p-adic group. The Principal Investigator will also pursue his work on unifying different methods of studying automorphic L-functions. Finally he will try to extend his result on the finiteness of poles of certain automorphic L- functions to a larger class of them. Generating functions of arithmetic functions are well known and powerful tools for the study of these functions. The deepest and most erudite of all these studies is the so called Langland's program. But the benefits of this program are very high. This research is in this area.