On the error term in Weyl's law for the Heisenberg manifolds

Abstract

For a fixed integer $l\ge 1$, 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 $3\le k\le 9.$ We shall also prove that the function $t^{-(l-1/4)}R(t)$ has a distribution function.

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