Meromorphic continuation of Minakshisundaram–Pleijel series for semisimple Lie groups

Floyd L. Williams

Vol. 182 (1998), No. 1, 137–156

DOI: 10.2140/pjm.1998.182.137

Abstract

An explicit meromorphic continuation of the Minakshisundaram-Pleijel zeta function for a compact Riemann surface has been obtained by B. Randol, using the Selberg trace formula. Such zeta functions can be defined in the context of a general rank 1 symmetric space form Γ∖G∕K. We find, similarly, their continuation to the full complex plane.

Milestones

Received: 25 October 1995

Revised: 22 April 1997

Published: 1 January 1998