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

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