Distributions of length multiplicities for negatively curved locally symmetric Riemannian manifolds
arXiv:math/0701239
Abstract
The aim of the present paper is to study the distributions of the length multiplicities for negatively curved locally symmetric Riemannian manifolds. In Theorem 2.1, we give upper bounds of the length multiplicities and the square sums of them for general (not necessarily compact) cases. Furthermore in Theorem 2.2, we obtain more precise estimates of the length multiplicities and the power sums of them for arithmetic surfaces whose fundamental groups are congruence subgroups of the modular group.
18 pages, This paper has been withdrawn by the author due to error in the proofs
References in corpus (4)
- Distribution of Eigenvalues for the Modular Group
- Trace formulae for three-dimensional hyperbolic lattices and application to a strongly chaotic tetrahedral billiard
- The correlation between multiplicities of closed geodesics on the modular surface
- Selberg's zeta functions for congruence subgroups of modular groups in SL(2,R) and SL(2,C)