This article is cited in 4 papers

On the Selberg Trace Formula for Strictly Hyperbolic Groups

D. A. Popov

A. N. Belozersky Institute of Physico-Chemical Biology, M. V. Lomonosov Moscow State University

Abstract: We show that, for the case of strictly hyperbolic groups, the right-hand side of the Selberg trace formula admits a representation in the form of a series in the eigenvalues of the Laplacian. The behavior of the Minakshisundaram function as $t\to0$ and $t\to\infty$ is studied. Countably many conditions satisfied by the spectrum of the Laplacian are obtained in explicit form.

Keywords: Selberg formula, strictly hyperbolic group, spectrum of the Laplacian.

UDC: 517.984.5

Received: 04.07.2011

DOI: 10.4213/faa3128

 English version: Functional Analysis and Its Applications, 2013, 47:4, 290–301

Bibliographic databases:

• 
• 
• 
• 
•