Temperedness of locally symmetric spaces: The product case

Tobias Weich; Lasse L. Wolf

doi:10.1007/s10711-024-00904-4

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arXiv · 2304.09573

Temperedness of locally symmetric spaces: The product case

Tobias Weich·Lasse L. Wolf

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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 $\Gamma$.

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BibTeX RIS

Tobias Weich, Lasse L. Wolf. 2023-04-19. Temperedness of locally symmetric spaces: The product case. https://doi.org/10.1007/s10711-024-00904-4

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