Mathematical Sciences: Plancherel Measures and Automorphic L-Functions

点击翻译按钮获取中文摘要

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.