On the stable trace formula for Sp4

Abstract

For many applications of the trace formula to problems in the theory of automorphic forms one needs to stabilize the trace formula. Such a stabilization has been achieved by Arthur, building on work of Langlands and Kottwitz, subject to conjectures for orbital integrals known as fundamental lemmas. For the group Sp4 the standard invariant fundamental lemma has been established by Hales. However, for the stabilization of the full trace formula one needs to prove a fundamental lemma for weighted orbital integrals on Sp4. We prove this weighted fundamental lemma and thereby make Arthur's stabilization of the Sp4 trace formula unconditional.