On Stablity and Endoscopic Transfer of Unipotent Orbital Integrals on P-adic Symplectic Groups

The theory of endoscopy is an intriguing part of the Langlands program, as it provides a way to attack the functoriality principle of Langlands for certain pairs of reductive groups $(G,H)$, in which $H$ is what is known as an endoscopic group for $G$. The starting point for this method is a close study of the relationship of orbital integrals on $G$ with stable orbital integrals on $H$. This volume investigates unipotent orbital integrals of spherical functions on $p$-adic symplectic groups. The results are then put into a conjectural framework, that predicts (for split classical groups) which linear combinations of unipotent orbital integrals are stable distributions.