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

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

2008-05-26

arxiv.org/abs/0805.3856v1

Mathematics

Optimization and Control

45 Pages

Scientific paper

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.

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