Approximating Fourier transformation of orbital integrals

Approximating Fourier transformation of orbital integrals

In this paper, we are concerned with orbital integrals on a class C of real reductive Lie groups with non-compact Iwasawa K-component. The class C contains all connected semisimple Lie groups with infinite center. We establish that any given orbital integral over general orbits with compactly supported continuous functions for a group G in C is convergent. Moreover, it is essentially the limit ...

On the Fourier transforms of weighted orbital integrals

Orbital Integrals Are Motivic

This article shows that under general conditions, p-adic orbital integrals of definable functions are represented by virtual Chow motives. This gives an explicit example of the philosophy of Denef and Loeser, which predicts that all “naturally occurring” p-adic integrals are motivic.

Good Orbital Integrals

This paper concerns a class of orbital integrals in Lie algebras over p-adic fields. The values of these orbital integrals at the unit element in the Hecke algebra count points on varieties over finite fields. The construction, which is based on motivic integration, works both in characteristic zero and in positive characteristic. As an application, the Fundamental Lemma for this class of integ...

Weighted orbital integrals

This is an expanded version of a survey talk given at the Conference on Representations of Real Reductive Lie Groups, June 4 to June 8, 2006, at the Snowbird Mountain Resort, Utah. We explain the definition of weighted orbital integrals and their Fourier transforms and report their known properties, leaving aside questions of endoscopy. We also announce some new results on those Fourier transfo...