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March, 2002 The Remainder in Weyl's Law for Heisenberg Manifolds
Yiannis N. Petridis, John A. Toth
J. Differential Geom. 60(3): 455-483 (March, 2002). DOI: 10.4310/jdg/1090351124

Abstract

We prove that the error term $R(\lambda)$ in Weyl's law is $\mathcal O_{\epsilon}(\lambda^{5/6 + \epsilon})$ 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 $\ll \lambda^{3/4 + \epsilon}$. We conjecture that $R(\lambda) = \mathcal{O}_{\epsilon}(\lambda^{3/4 + \epsilon})$ is a sharp deterministic upper bound for Heisenberg three-manifolds.

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Yiannis N. Petridis. John A. Toth. "The Remainder in Weyl's Law for Heisenberg Manifolds." J. Differential Geom. 60 (3) 455 - 483, March, 2002. https://doi.org/10.4310/jdg/1090351124

Information

Published: March, 2002
First available in Project Euclid: 20 July 2004

zbMATH: 1066.58017
MathSciNet: MR1950173
Digital Object Identifier: 10.4310/jdg/1090351124

Rights: Copyright © 2002 Lehigh University

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Vol.60 • No. 3 • March, 2002
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