Generalized Orbital Integrals of Some Euler–Poincaré Functions of a Reductive p-Adic Group,

Schneider and Stuhler have defined Euler–Poincaré 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–Poincaré functions of tempered representations using the Arthur local trace formula.