Temperedness of locally symmetric spaces: The product case

Abstract

Let $X=X_1\times X_2$ be a product of two rank one symmetric spaces of non-compact type and $\Gamma$ a torsion-free discrete subgroup in $G_1\times G_2$. We show that the spectrum of $\Gamma \backslash X$ is related to the asymptotic growth of $\Gamma$ in the two direction defined by the two factors. We obtain that $L^2(\Gamma \backslash G)$ is tempered for large class of $\Gamma$.

17 pages, 1 figure

References in corpus (1)

• Higher rank quantum-classical correspondence

Cited by in corpus (1)

• $L^2$-spectrum, growth indicator function and critical exponent on locally symmetric spaces