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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The remainder in Weyl's law for $n$-dimensional Heisenberg manifolds


Authors: Mahta Khosravi and Yiannis N. Petridis
Journal: Proc. Amer. Math. Soc. 133 (2005), 3561-3571
MSC (2000): Primary 35P20; Secondary 58J50, 11N37
Published electronically: June 28, 2005
MathSciNet review: 2163591
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Abstract: We prove that the error term in Weyl's law for `rational' $(2n+1)$-dimensional Heisenberg manifolds is of order $O(t^{n-{7}/{41}})$. In the `irrational' case, for generic $(2n+1)$-dimensional Heisenberg manifolds with $n>1$, we prove that the error term is of the order $O(t^{n-{1}/{4}}\log t)$. The polynomial growth is optimal.


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Additional Information

Mahta Khosravi
Affiliation: Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. West, Montreal, Quebec, Canada H3A 2K6
Email: khosravi@math.mcgill.ca

Yiannis N. Petridis
Affiliation: Department of Mathematics and Computer Science, City University of New York, Lehman College, 250 Bedford Park Boulevard West, Bronx, New York 10468-1589 – and – The Graduate Center, Mathematics Ph.D. Program, 365 Fifth Avenue, Room 4208, New York, New York 10016-4309
Email: petridis@comet.lehman.cuny.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08155-4
PII: S 0002-9939(05)08155-4
Received by editor(s): July 9, 2004
Published electronically: June 28, 2005
Additional Notes: The first author would like to acknowledge the financial support of McGill University through the McConnell McGill Major fellowship. The second author was partially supported by NSF grant DMS 0401318, PSC CUNY Research Award, No. 60007-33-34, and a George Shuster Fellowship at Lehman College
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.