D. A. Popov, “Explicit Formula for the Spectral Counting Function of the Laplace Operator on a Compact Riemannian Surface of Genus <nobr>$g>1$</nobr>”, Funktsional. Anal. i Prilozhen., 2012, Volume 46, Issue 2,Pages <nobr>66

This article is cited in 3 papers

Explicit Formula for the Spectral Counting Function of the Laplace Operator on a Compact Riemannian Surface of Genus $g>1$

D. A. Popov^ab

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

Abstract: Let the standard Riemannian metric of constant curvature $K=-1$ be given on a compact Riemannian surface of genus $g>1$. Under this condition, for a class of strictly hyperbolic Fuchsian groups, we obtain an explicit expression for the spectral counting function of the Laplace operator in the form of a series over the zeros of the Selberg zeta function.

Keywords: Selberg zeta function, spectral counting function, strictly hyperbolic group.

UDC: 517.984.5

Received: 24.02.2011

DOI: 10.4213/faa3073