 
Summary: Germ expansions for real groups
James Arthur*
Contents
Introduction
§1 Singular invariant distributions
§2 Invariant germ expansions
§3 Weighted orbital integrals
§4 Spaces of formal germs
§5 Statement of the general germ expansions
§6 Some consequences of the induction hypothesis
§7 An estimate
§8 The mapping M
§9 Completion of the proof
§10 Invariant distributions IM (, f)
§11 Supplementary properties
* Supported in part by a Guggenheim Fellowship, the Institute for Advanced Study, and an NSERC Operating
Grant.
Germ expansions for real groups 2
Introduction
Suppose that G is a connected reductive group over a local field F of characteristic 0. The study of harmonic
