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Article: On the number of sign changes of hecke eigenvalues of newforms

TitleOn the number of sign changes of hecke eigenvalues of newforms
Authors
KeywordsHecke eigenvalues
Sign changes
Issue Date2008
PublisherAustralian Mathematical Society. The Journal's web site is located at http://www.austms.org.au/Publ/JAustMS/
Citation
Journal Of The Australian Mathematical Society, 2008, v. 85 n. 1, p. 87-94 How to Cite?
AbstractWe show that, for every x exceeding some explicit bound depending only on k and N, there are at least C(k,N)x/log17x positive and negative coefficients a(n) with n ≤ x in the Fourier expansion of any non-zero cuspidal Hecke eigenform of even integral weight k ≥ 2 and squarefree level N that is a newform, where C(k,N) depends only on k and N. From this we deduce the existence of a sign change in a short interval. © 2008 Copyright 2008 Australian Mathematical Society.
Persistent Identifierhttp://hdl.handle.net/10722/58959
ISSN
2015 Impact Factor: 0.443
2015 SCImago Journal Rankings: 0.255
ISI Accession Number ID
Funding AgencyGrant Number
ARCD110556431
Funding Information:

The third author was supported in part by ARC grant D110556431 during the preparation of this paper,

References

 

DC FieldValueLanguage
dc.contributor.authorKohnen, Wen_HK
dc.contributor.authorLau, YKen_HK
dc.contributor.authorShparlinski, IEen_HK
dc.date.accessioned2010-05-31T03:40:23Z-
dc.date.available2010-05-31T03:40:23Z-
dc.date.issued2008en_HK
dc.identifier.citationJournal Of The Australian Mathematical Society, 2008, v. 85 n. 1, p. 87-94en_HK
dc.identifier.issn1446-7887en_HK
dc.identifier.urihttp://hdl.handle.net/10722/58959-
dc.description.abstractWe show that, for every x exceeding some explicit bound depending only on k and N, there are at least C(k,N)x/log17x positive and negative coefficients a(n) with n ≤ x in the Fourier expansion of any non-zero cuspidal Hecke eigenform of even integral weight k ≥ 2 and squarefree level N that is a newform, where C(k,N) depends only on k and N. From this we deduce the existence of a sign change in a short interval. © 2008 Copyright 2008 Australian Mathematical Society.en_HK
dc.languageengen_HK
dc.publisherAustralian Mathematical Society. The Journal's web site is located at http://www.austms.org.au/Publ/JAustMS/en_HK
dc.relation.ispartofJournal of the Australian Mathematical Societyen_HK
dc.rightsJournal of the Australian Mathematical Society. Copyright © Cambridge University Press.en_HK
dc.subjectHecke eigenvaluesen_HK
dc.subjectSign changesen_HK
dc.titleOn the number of sign changes of hecke eigenvalues of newformsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1446-7887 &volume=85&spage=87&epage=94&date=2008&atitle=On+the+number+of+sign+changes+of+Hecke+eigenvalues+of+newformsen_HK
dc.identifier.emailLau, YK:yklau@maths.hku.hken_HK
dc.identifier.authorityLau, YK=rp00722en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1017/S1446788708000323en_HK
dc.identifier.scopuseid_2-s2.0-56749161103en_HK
dc.identifier.hkuros155619en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-56749161103&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume85en_HK
dc.identifier.issue1en_HK
dc.identifier.spage87en_HK
dc.identifier.epage94en_HK
dc.identifier.isiWOS:000262919600007-
dc.publisher.placeAustraliaen_HK
dc.identifier.scopusauthoridKohnen, W=7003954289en_HK
dc.identifier.scopusauthoridLau, YK=35724053400en_HK
dc.identifier.scopusauthoridShparlinski, IE=7005075576en_HK

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