标题： 自守$L$\snug -函数，交错算子，以及$p$\snug -进群的不可约温驯表示 显示英文标题

标题： Automorphic $L$\snug-functions, intertwining operators, and the irreducible tempered representations of $p$\snug-adic groups

摘要： 我们对与连通的重ductive $p$-adic 群相关的缠绕算子理论及其与自守$L$-函数的联系进行了综述性介绍。我们的目的是阐明调和分析与算术之间的关系。特别是，我们描述了 Plancherel 测度理论如何使我们能够计算某些局部 Langlands$L$-函数。为了更加自成体系，我们简要介绍了 Langlands纲领。这里也讨论了$R$-群和椭圆表示的理论。最后，我们给出一个例子，说明扭曲端几何学理论在确定所涉及的缠绕算子和局部 Langlands$L$-函数的极点方面起着关键作用。修订后的版本将作为会议 “Teoria de Representaciones de Grupos Algebraicos Sobre Cuerpos Locales y Aplicaciones”（C. Bushnell, P. Kutzko, J. Pantoja, J. Soto Andrade 编）文集的一章发表。 显示英文摘要

摘要： We give an expository account of the theory of intertwining operators for connected reductive $p$--adic groups, and their connection with automorphic $L$--functions. Our purpose is to illustrate the relation between harmonic analysis and arithmetic. In particular, we describe how the theory of Plancherel measures allows us to compute certain local Langlands $L$--functions. In order to be more self contained, we give a brief introduction to the Langlands program. The theory of $R$--groups and elliptic representations is treated here as well. Finally, we give an example which illustrates how the theory of twisted endoscopy plays a crucial role in determining the poles of both the intertwining operators and the local Langlands $L$--functions in question. A version of this manuscript, in revised form, will appear as a chapter in the proceedings of the conference ``Teoria de Representaciones de Groupos Algebraicos Sobre Cuerpos Locales y Applicationes'' (C. Bushnell, P. Kutzko, J. Pantoja, J. Soto Andrade eds.).