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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
Contributor : Hong-Wei ZHANG Connect in order to contact the contributor
Submitted on : Thursday, July 22, 2021 - 4:18:31 PM
Last modification on : Wednesday, August 31, 2022 - 1:04:05 PM

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AZ2021.pdf
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• HAL Id : hal-02865274, version 2

### Citation

Jean-Philippe Anker, Hong-Wei Zhang. Bottom of the $L^2$ spectrum of the Laplacian on locally symmetric spaces. Geometriae Dedicata, 2022, 216 (1), paper 3. ⟨hal-02865274v2⟩

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