On an Analog of Selberg's Eigenvalue Conjecture for SL₃(Z)

1998/11/27 by Sultan Catto, Jonathan Huntley, Catto, Sultan +5
Mathematics · #FOS: Mathematics #Spectral Theory (math.SP) #math.SP

paper · pdf · doi:10.48550/arxiv.math/9811158

arxiv created 1998/11/27 · arxiv updated 2009/11/30

Abstract

Let H be the homogeneous space associated to the group PGL₃(R). Let X=Γ/H where Γ=SL₃(Z) and consider the first non-trivial eigenvalue λ₁ of the Laplacian on L²(X). Using geometric considerations, we prove the inequality λ₁<pi²/10. Since the continuous spectrum is represented by the band [1,∞), our bound on λ₁ can be viewed as an analogue of Selberg's eigenvalue conjecture for quotients of the hyperbolic half space.

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