Distributions of length multiplicities for negatively curved locally symmetric Riemannian manifolds

Details Distributions of length multiplicities for negatively curved locally symmetric Riemannian manifolds Distributions of length multiplicities for negatively curved locally symmetric Riemannian manifolds

2007-01-09

arxiv.org/abs/math/0701239v2

Mathematics

Spectral Theory

18 pages

Scientific paper

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.

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