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are obtained by integrating f with respect to the invariant measure on the conjugacy class of y. They are of considerable importance for the harmonic analysis of G(F). Invariant orbital integrals are also of interest because they occur on the geometric side of the trace formula, in the case of compact quotient. For the general trace formula, the analogous(More)
Preface Following the explicit instructions of the organizers, I have tried to write an article that is suitable for a general mathematical audience. It contains some analogies and metaphors that might even be put to nonmathematicians. I hope that experts will be tolerant of the inevitable simplifications. The principle of functoriality is one of the(More)
Introduction Suppose that G is a semisimple Lie group and that F is a discrete subgroup of G. We assume that F is an arithmetic subgroup defined by congruence conditions , and for simplicity, suppose also that G is contained in a simply connected complex group. A fundamental problem is to decompose the regular representation of G on L2(f\G) into irreducible(More)
The purpose of this article is to discuss some questions in the harmonic analysis of real and padic groups. We shall be particularly concerned with the properties of a certain family of invariant distributions. These distributions arose naturally in a global context, as the terms on the geometric side of the trace formula. However, they are purely local(More)