%0 Journal Article
%T On the error term in Weyl's law for the Heisenberg manifolds
%A Wenguang Zhai
%J Mathematics
%D 2008
%I arXiv
%X For a fixed integer $l\geq 1$, let $R(t)$ denote the error term in the Weyl's law of a $(2l+1)$-dimensional Heisenberg manifold with the metric $g_l.$ In this paper we shall prove the asymptotic formula of the $k$-th power moment for any integers $3\leq k\leq 9.$ We shall also prove that the function $t^{-(l-1/4)}R(t)$ has a distribution function.
%U http://arxiv.org/abs/0805.3856v1