A Conjecture about the Analytical Behaviour of Eisenstein Series

Abstract

This paper will formulate and offer evidence for a conjecture on the analytical behaviour of residual Eisenstein series in the positive Weyl chamber. It should play a major role in an also conjectural Paley-Wiener theorem about the Schwartz space of arithmetic quotients. If things work out as I expect, this development should be logically independent of Chapter 7 of [Langlands:1976], and in the end one should obtain a new proof of Langlands’ completeness theorem.