{"date_updated":"2024-04-10T13:48:17Z","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"In this short note we observe, on locally symmetric spaces of higher rank, a\r\nconnection between the growth indicator function introduced by Quint and the\r\nmodified critical exponent of the Poincar\\'e series equipped with the\r\npolyhedral distance. As a consequence, we provide a different characterization\r\nof the bottom of the $L^2$-spectrum of the Laplace-Beltrami operator in terms\r\nof the growth indicator function. Moreover, we explore the relationship between\r\nthese three objects and the temperedness."}],"publication":"arXiv:2311.11770","title":"$L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces","user_id":"45027","year":"2023","author":[{"last_name":"Wolf","full_name":"Wolf, Lasse L.","first_name":"Lasse L."},{"first_name":"Hong-Wei","full_name":"Zhang, Hong-Wei","last_name":"Zhang"}],"status":"public","_id":"53404","external_id":{"arxiv":["2311.11770"]},"date_created":"2024-04-10T13:45:59Z","department":[{"_id":"10"},{"_id":"548"}],"citation":{"ama":"Wolf LL, Zhang H-W. $L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces. <i>arXiv:231111770</i>. Published online 2023.","bibtex":"@article{Wolf_Zhang_2023, title={$L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces}, journal={arXiv:2311.11770}, author={Wolf, Lasse L. and Zhang, Hong-Wei}, year={2023} }","ieee":"L. L. Wolf and H.-W. Zhang, “$L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces,” <i>arXiv:2311.11770</i>. 2023.","short":"L.L. Wolf, H.-W. Zhang, ArXiv:2311.11770 (2023).","apa":"Wolf, L. L., &#38; Zhang, H.-W. (2023). $L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces. In <i>arXiv:2311.11770</i>.","mla":"Wolf, Lasse L., and Hong-Wei Zhang. “$L^2$-Spectrum, Growth Indicator Function and Critical Exponent on  Locally Symmetric Spaces.” <i>ArXiv:2311.11770</i>, 2023.","chicago":"Wolf, Lasse L., and Hong-Wei Zhang. “$L^2$-Spectrum, Growth Indicator Function and Critical Exponent on  Locally Symmetric Spaces.” <i>ArXiv:2311.11770</i>, 2023."},"type":"preprint"}