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We establish a sharp estimate on the size of the spectral clusters of theLandau Hamiltonian with $L^p$ potentials in two dimensions as the cluster indextends to infinity. In three dimensions, we prove a new limiting absorptionprinciple as well as a unique continuation theorem. The results generalize tohigher dimensions.

Sharp spectral estimates for the perturbed Landau Hamiltonian with $L^p$ potentials