Bottom of the $L^2$ spectrum of the Laplacian on locally symmetric spaces

Jean-Philippe Anker; Hong-Wei Zhang

doi:10.1007/s10711-021-00662-7

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arXiv · 2006.06473

Bottom of the $L^2$ spectrum of the Laplacian on locally symmetric spaces

Jean-Philippe Anker·Hong-Wei Zhang

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Abstract

We estimate the bottom of the $L^2$ spectrum of the Laplacian on locally symmetric spaces in terms of the critical exponents of appropriate Poincar\'e series. Our main result is the higher rank analog of a characterization due to Elstrodt, Patterson, Sullivan and Corlette in rank one. It improves upon previous results obtained by Leuzinger and Weber in higher rank.

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BibTeX RIS

Jean-Philippe Anker, Hong-Wei Zhang. 2020-06-11. Bottom of the $L^2$ spectrum of the Laplacian on locally symmetric spaces. https://doi.org/10.1007/s10711-021-00662-7

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