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

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 Poincaré 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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https://hal.archives-ouvertes.fr/hal-02865274
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Submitted on : Thursday, June 11, 2020 - 4:03:11 PM
Last modification on : Tuesday, October 12, 2021 - 5:20:53 PM

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  • HAL Id : hal-02865274, version 1

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Jean-Philippe Anker, Hong-Wei Zhang. Bottom of the $L^2$ spectrum of the Laplacian on locally symmetric spaces. 2020. ⟨hal-02865274v1⟩

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