Distributions of length multiplicities for negatively curved locally symmetric Riemannian manifolds

2007/01/09 by Yasufumi Hashimoto, Hashimoto, Yasufumi
Mathematics · #11F72 #11M36 #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Number Theory (math.NT) #Spectral Theory (math.SP) #math.NT #math.SP #msc:11F72 #msc:11M36

paper · pdf · doi:10.48550/arxiv.math/0701239

18 pages, This paper has been withdrawn by the author due to error in the proofs

openalex publication_date 2007/01/09 · arxiv created 2015/02/09 · arxiv updated 2015/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Selberg's zeta functions for congruence subgroups of modular groups in SL(2,R) and SL(2,C)

Related

• On Length Sets of Subarithmetic Hyperbolic Manifolds
• On Small Gaps in the Length Spectrum
• Counting arcs in negative curvature
• On the fields generated by the lengths of closed geodesics in locally symmetric spaces
• On multiplicities in length spectra of semi-arithmetic hyperbolic surfaces