$L^2$-spectrum, growth indicator function and critical exponent on locally symmetric spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916449113604096 |
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| author | Wolf, Lasse L. Zhang, Hong-Wei |
| author_facet | Wolf, Lasse L. Zhang, Hong-Wei |
| contents | In this short note we observe, on locally symmetric spaces of higher rank, a connection between the growth indicator function introduced by Quint and the modified critical exponent of the Poincaré series equipped with the polyhedral distance. As a consequence, we provide a different characterization of the bottom of the $L^2$-spectrum of the Laplace-Beltrami operator in terms of the growth indicator function. Moreover, we explore the relationship between these three objects and the temperedness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11770 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $L^2$-spectrum, growth indicator function and critical exponent on locally symmetric spaces Wolf, Lasse L. Zhang, Hong-Wei Spectral Theory 22E40, A7A10, 58J50 In this short note we observe, on locally symmetric spaces of higher rank, a connection between the growth indicator function introduced by Quint and the modified critical exponent of the Poincaré series equipped with the polyhedral distance. As a consequence, we provide a different characterization of the bottom of the $L^2$-spectrum of the Laplace-Beltrami operator in terms of the growth indicator function. Moreover, we explore the relationship between these three objects and the temperedness. |
| title | $L^2$-spectrum, growth indicator function and critical exponent on locally symmetric spaces |
| topic | Spectral Theory 22E40, A7A10, 58J50 |
| url | https://arxiv.org/abs/2311.11770 |