Horizontal lift of the Brownian motion on the hyperbolic plane and the Selberg trace formula

By using an explicit representation for the horizontal lift of the Brownian motion on the Poincaré upper half-plane H2, we show an expression for the heat kernel for the de Rham–Kodaira Laplacian on H2. We apply the result to a study on the Selberg trace formula. © 2006 Elsevier Inc. All rights reserved.