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Let R(T) be the error term in Weyl's law for the (2l + 1)-dimensional Heisenberg manifold (H l/Γ, gl). In this paper, several results on the sign changes and odd moments of R(t) are proved. In particular, it is proved that for some sufficiently large constant c, R(t) changes sign in the interval for all large T. Moreover, for a small constant c1 there exist infinitely many subintervals in [T, 2T] of length such that holds on each of these subintervals. © 2012 American Mathematical Society.published_or_final_versio

Sign changes of the error term in Weyl’s law for Heisenberg manifolds