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On an Analog of Selberg's Eigenvalue Conjecture for SL_3(Z)

Sultan Catto·Jonathan Huntley·Jay Jorgenson·David Tepper
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Abstract

Let H be the homogeneous space associated to the group PGL_3(R). Let X=Γ/H where Γ=SL_3(Z) and consider the first non-trivial eigenvalue λ_1 of the Laplacian on L^2(X). Using geometric considerations, we prove the inequality λ_1<pi^2/10. Since the continuous spectrum is represented by the band [1,\infty), our bound on λ_1 can be viewed as an analogue of Selberg's eigenvalue conjecture for quotients of the hyperbolic half space.

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Sultan Catto, Jonathan Huntley, Jay Jorgenson, David Tepper. 1998-11-27. On an Analog of Selberg's Eigenvalue Conjecture for SL_3(Z). https://arxiv.org/abs/math/9811158

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