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.

arXiv commentTo appear in Geometriae Dedicata

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