Generalized orbital integrals of some Euler-Poincare functions of a reductive p-adic group

Abstract

Schneider and Stuhler have defined Euler-Poincare functions of irreducible representations of reductive p-adic groups and calculated their orbital integrals. Orbital integrals belong to a larger family of invariant distributions appearing in the geometric side of the Arthur-Selberg trace formula. We calculate the value of these distributions on the Euler-Poincare functions of tempered representations using the Arthur local trace formula. (C) 2001 Academic Press.