The Selberg trace formula. VII. Application of the truncation process to the continuous spectrum

M. Scott Osborne and Garth William Warner, Jr.

Vol. 140 (1989), No. 2, 263–352

DOI: 10.2140/pjm.1989.140.263

Abstract

This is the seventh in a projected series of papers in which we plan to come to grips with the Selberg trace formula, the ultimate objective being a reasonably explicit expression. As the title suggests, our goal in this work is to prepare the stage for the complete delineation of the contribution to the trace coming from the continuous spectrum, concentrating here on the role played by the truncation process. In our next publication, we shall finish the investigation, setting down the precise form of the various terms in all detail.

Mathematical Subject Classification 2000

Primary: 22E45

Secondary: 11F72, 22E40

Milestones

Received: 28 October 1987

Published: 1 December 1989