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Article: On a variance of Hecke eigenvalues in arithmetic progressions
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TitleOn a variance of Hecke eigenvalues in arithmetic progressions
 
AuthorsLau, YK1
Zhao, L1
 
KeywordsDivisor function
Fourier coefficient
Hecke eigenvalue
Holomorphic cusp form
Variance
 
Issue Date2012
 
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt
 
CitationJournal of Number Theory, 2012, v. 132 n. 5, p. 869-887 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.jnt.2011.12.011
 
AbstractLet a(n) be the eigenvalue of a holomorphic Hecke eigenform f under the nth Hecke operator. We derive asymptotic formulae for the variance ∑ b=1 q|∑ n≤Xn≡ b(modq)a(n)| 2 when X 1/4+ε≤q≤X 1/2-ε or X 1/2+ε≤q≤X 1-ε, that exhibit distinct behavior. The analogous problem for the divisor function will be studied as well. © 2012 Elsevier Inc.
 
ISSN0022-314X
2013 Impact Factor: 0.524
 
DOIhttp://dx.doi.org/10.1016/j.jnt.2011.12.011
 
ISI Accession Number IDWOS:000301324400001
Funding AgencyGrant Number
Research Grants Council of the Hong Kong Special Administrative Region, ChinaHKU702308P
Funding Information:

The authors wish to thank the referees for their readings, the explanatory viewpoint in Remark 3 and criticism. Lau is supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU702308P).

 
ReferencesReferences in Scopus
 
DC FieldValue
dc.contributor.authorLau, YK
 
dc.contributor.authorZhao, L
 
dc.date.accessioned2012-08-08T08:41:09Z
 
dc.date.available2012-08-08T08:41:09Z
 
dc.date.issued2012
 
dc.description.abstractLet a(n) be the eigenvalue of a holomorphic Hecke eigenform f under the nth Hecke operator. We derive asymptotic formulae for the variance ∑ b=1 q|∑ n≤Xn≡ b(modq)a(n)| 2 when X 1/4+ε≤q≤X 1/2-ε or X 1/2+ε≤q≤X 1-ε, that exhibit distinct behavior. The analogous problem for the divisor function will be studied as well. © 2012 Elsevier Inc.
 
dc.description.natureLink_to_subscribed_fulltext
 
dc.identifier.citationJournal of Number Theory, 2012, v. 132 n. 5, p. 869-887 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.jnt.2011.12.011
 
dc.identifier.citeulike10326545
 
dc.identifier.doihttp://dx.doi.org/10.1016/j.jnt.2011.12.011
 
dc.identifier.epage887
 
dc.identifier.hkuros206537
 
dc.identifier.isiWOS:000301324400001
Funding AgencyGrant Number
Research Grants Council of the Hong Kong Special Administrative Region, ChinaHKU702308P
Funding Information:

The authors wish to thank the referees for their readings, the explanatory viewpoint in Remark 3 and criticism. Lau is supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU702308P).

 
dc.identifier.issn0022-314X
2013 Impact Factor: 0.524
 
dc.identifier.issue5
 
dc.identifier.scopuseid_2-s2.0-84863421506
 
dc.identifier.spage869
 
dc.identifier.urihttp://hdl.handle.net/10722/156279
 
dc.identifier.volume132
 
dc.languageeng
 
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt
 
dc.publisher.placeUnited States
 
dc.relation.ispartofJournal of Number Theory
 
dc.relation.referencesReferences in Scopus
 
dc.subjectDivisor function
 
dc.subjectFourier coefficient
 
dc.subjectHecke eigenvalue
 
dc.subjectHolomorphic cusp form
 
dc.subjectVariance
 
dc.titleOn a variance of Hecke eigenvalues in arithmetic progressions
 
dc.typeArticle
 
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Author Affiliations
  1. The University of Hong Kong