A bound for the ratio of consecutive eigenvalues of the hyperbolic Laplacian for the modular groups

Authors
Chinen, K
Citation
K. Chinen, A bound for the ratio of consecutive eigenvalues of the hyperbolic Laplacian for the modular groups, FORUM MATH, 13(5), 2001, pp. 685-720
Citations number
18
Categorie Soggetti
Mathematics
Journal title
FORUM MATHEMATICUM
ISSN journal
09337741 → ACNP
Volume
13
Issue
5
Year of publication
2001
Pages
685 - 720
Database
ISI
SICI code
0933-7741(2001)13:5<685:ABFTRO>2.0.ZU;2-N
Abstract
The problem of estimating the ratio of consecutive eigenvalues of the Eucli dean Laplacian has been considered for many years. This paper attempts to d educe similar results in the case of the hyperbolic Laplacian for all subgr oups of the full modular group. The Selberg trace formula is used as a main tool, the test function and the method of estimation are a little differen t from previously known results.