Memoirs of the American Mathematical Society 2009; 127 pp; softcover Volume: 201 ISBN10: 0821840444 ISBN13: 9780821840443 List Price: US$71 Individual Members: US$42.60 Institutional Members: US$56.80 Order Code: MEMO/201/946
 The purpose of this Memoir is to define and study multivariable Eisenstein series attached to heat kernels. Fundamental properties of heat Eisenstein series are proved, and conjectural behavior, including their role in spectral expansions, are stated. Table of Contents  Introduction
 Notation and terminology
 Estimates on \({\rm SL}_{n}\) and parabolics
 Eisenstein series
 Adjointness and inversion relations
 Applications of the heat equation
 Appendix. The heat kernel
 Bibliography
 Index
