The remainder in Weyl's law for n-dimensional Heisenberg manifolds

摘要

We prove that the error term in Weyl's law for 'rational' (2n + 1)dimensional Heisenberg manifolds is of order O(t(n-7/41)). In the 'irrational' case, for generic (2n + 1)-dimensional Heisenberg manifolds with n > 1, we prove that the error term is of the order O(t(n-1/4) log t). The polynomial growth is optimal.