On an Analog of Selberg's Eigenvalue Conjecture for SL3(Z)
Sultan Catto, Jonathan Huntley, Jay Jorgenson, David Tepper
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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