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In this short note we prove a sharp lower bound for the second moment of alattice Voronoi cell in terms of the respective covering radius. This gives anaffirmative answer to a conjecture by Haviv, Lyubashevsky and Regev. We alsocharacterize those lattice Voronoi cells for which this lower bound isattained.

A proof of a conjecture by Haviv, Lyubashevsky and Regev on the second moment of a lattice Voronoi cell