The remainder in Weyl's law for -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

DOI:
https://doi.org/10.1090/S0002-9939-05-08155-4

Published electronically:
June 28, 2005

MathSciNet review:
2163591

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the error term in Weyl's law for `rational' -dimensional Heisenberg manifolds is of order . In the `irrational' case, for generic -dimensional Heisenberg manifolds with , we prove that the error term is of the order . 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:
https://doi.org/10.1090/S0002-9939-05-08155-4

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.