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Article: On a variance of Hecke eigenvalues in arithmetic progressions

TitleOn a variance of Hecke eigenvalues in arithmetic progressions
Authors
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
Citation
Journal of Number Theory, 2012, v. 132 n. 5, p. 869-887 How to Cite?
Abstract
Let 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.
Persistent Identifierhttp://hdl.handle.net/10722/156279
ISSN
2013 Impact Factor: 0.524
ISI Accession Number ID
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).

References

 

DC FieldValueLanguage
dc.contributor.authorLau, YKen_US
dc.contributor.authorZhao, Len_US
dc.date.accessioned2012-08-08T08:41:09Z-
dc.date.available2012-08-08T08:41:09Z-
dc.date.issued2012en_US
dc.identifier.citationJournal of Number Theory, 2012, v. 132 n. 5, p. 869-887en_US
dc.identifier.issn0022-314Xen_US
dc.identifier.urihttp://hdl.handle.net/10722/156279-
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.en_US
dc.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnten_US
dc.relation.ispartofJournal of Number Theoryen_US
dc.subjectDivisor functionen_US
dc.subjectFourier coefficienten_US
dc.subjectHecke eigenvalueen_US
dc.subjectHolomorphic cusp formen_US
dc.subjectVarianceen_US
dc.titleOn a variance of Hecke eigenvalues in arithmetic progressionsen_US
dc.typeArticleen_US
dc.identifier.emailLau, YK: yklau@maths.hku.hken_US
dc.identifier.emailZhao, L: zhaolilu@gmail.com-
dc.identifier.authorityLau, YK=rp00722en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/j.jnt.2011.12.011en_US
dc.identifier.scopuseid_2-s2.0-84863421506en_US
dc.identifier.hkuros206537-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-84856439849&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume132en_US
dc.identifier.issue5en_US
dc.identifier.spage869en_US
dc.identifier.epage887en_US
dc.identifier.isiWOS:000301324400001-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridZhao, L=54942149800en_US
dc.identifier.scopusauthoridLau, YK=35724053400en_US
dc.identifier.citeulike10326545-

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