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ISSN 1088-6850(e) ISSN 0002-9947(p)

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

Authors: Kai-Man Tsang and Wenguang Zhai
Journal: Trans. Amer. Math. Soc. 364 (2012), 2647-2666
MSC (2010): Primary 11N37, 35P20, 58J50
Posted: January 19, 2012
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Abstract: Let be the error term in Weyl's law for the -dimen-
sional Heisenberg manifold $(H_l/\Gamma , g_l)$ . In this paper, several results on the sign changes and odd moments of are proved. In particular, it is proved that for some sufficiently large constant , changes sign in the interval $[T, T + c \sqrt T]$ for all large . Moreover, for a small constant there exist infinitely many subintervals in of length $c_1 \sqrt T \log ^{-5} T$ such that $\pm R(t)>c_1t^{l - 1/4}$ holds on each of these subintervals.

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