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

TitleSign changes of the error term in Weyl's law for Heisenberg manifolds
Authors
Tsang, KMZhai, W
KeywordsError Term
Sign Change
Voronoi's Formula
Weyl's Law
Words And Phrases. Heisenberg Manifold
Issue Date2012
PublisherAmerican Mathematical Society. The Journal's web site is located at http://www.ams.org/publications/journals/journalsframework/tran
Citation
Transactions of The American Mathematical Society, 2012, v. 364 n. 5, p. 2647-2666 How to Cite?
DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05437-7
AbstractLet R(T) be the error term in Weyl's law for the (2l + 1)-dimensional Heisenberg manifold (H l/Γ, gl). In this paper, several results on the sign changes and odd moments of R(t) are proved. In particular, it is proved that for some sufficiently large constant c, R(t) changes sign in the interval for all large T. Moreover, for a small constant c1 there exist infinitely many subintervals in [T, 2T] of length such that holds on each of these subintervals. © 2012 American Mathematical Society.
Persistent Identifierhttp://hdl.handle.net/10722/156281
ISSN
0002-9947
2021 Impact Factor: 1.351
2020 SCImago Journal Rankings: 1.798
ISI Accession Number ID
WOS:000302826600019
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorTsang, KMen_US
dc.contributor.authorZhai, Wen_US
dc.date.accessioned2012-08-08T08:41:10Z-
dc.date.available2012-08-08T08:41:10Z-
dc.date.issued2012en_US
dc.identifier.citationTransactions of The American Mathematical Society, 2012, v. 364 n. 5, p. 2647-2666en_US
dc.identifier.issn0002-9947en_US
dc.identifier.urihttp://hdl.handle.net/10722/156281-
dc.description.abstractLet R(T) be the error term in Weyl's law for the (2l + 1)-dimensional Heisenberg manifold (H l/Γ, gl). In this paper, several results on the sign changes and odd moments of R(t) are proved. In particular, it is proved that for some sufficiently large constant c, R(t) changes sign in the interval for all large T. Moreover, for a small constant c1 there exist infinitely many subintervals in [T, 2T] of length such that holds on each of these subintervals. © 2012 American Mathematical Society.en_US
dc.languageengen_US
dc.publisherAmerican Mathematical Society. The Journal's web site is located at http://www.ams.org/publications/journals/journalsframework/tran-
dc.relation.ispartofTransactions of the American Mathematical Societyen_US
dc.rightsFirst published in Transactions of the American Mathematical Society in 2012, v. 364 n. 5, p. 2647-2666, published by the American Mathematical Society-
dc.subjectError Termen_US
dc.subjectSign Changeen_US
dc.subjectVoronoi's Formulaen_US
dc.subjectWeyl's Lawen_US
dc.subjectWords And Phrases. Heisenberg Manifolden_US
dc.titleSign changes of the error term in Weyl's law for Heisenberg manifoldsen_US
dc.typeArticleen_US
dc.identifier.emailTsang, KM:kmtsang@maths.hku.hken_US
dc.identifier.authorityTsang, KM=rp00793en_US
dc.description.naturepublished_or_final_versionen_US
dc.identifier.doi10.1090/S0002-9947-2012-05437-7en_US
dc.identifier.scopuseid_2-s2.0-84856635992en_US
dc.identifier.hkuros221466-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-84856635992&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume364en_US
dc.identifier.issue5en_US
dc.identifier.spage2647en_US
dc.identifier.epage2666en_US
dc.identifier.eissn1088-6850-
dc.identifier.isiWOS:000302826600019-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridTsang, KM=7201554731en_US
dc.identifier.scopusauthoridZhai, W=7102239162en_US
dc.identifier.issnl0002-9947-

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