Iwahori-Hecke algebra and unramified local L-functions

Abstract

In this paper, we compute the Hecke action of a certain test function on the space of an unramified principal series of a connected reductive group over a non-archimedean local field by using the theory of Iwahori--Hecke algebra. As an application, we obtain a new expression of the local L-functions of unramified representations.

arXiv comment41 pages, 1 table, proofs were simplified according to the suggestion of Thomas Haines