# The remainder in Weyl's law for Heisenberg manifolds. II

@inproceedings{Petridis2002TheRI, title={The remainder in Weyl's law for Heisenberg manifolds. II}, author={Yiannis N. Petridis and Derrick Chung and John A. Toth}, year={2002} }

- Published 2002
DOI:10.4310/jdg/1090351124

We prove that the error term R(λ) in Weyl’s law is O� (λ5/6+� ) for certain three-dimensional Heisenberg manifolds. We also show that the L 2 -norm of the Weyl error term integrated over the moduli space of left-invariant Heisenberg metrics is � λ 3/4+� . We conjecture that R(λ )= O� (λ 3/4+� )i s a sharp deterministic upper bound for Heisenberg three-manifolds.

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## A lower bound for the error term in Weyl’s law for certain Heisenberg manifolds

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