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dc.contributor.authorSaias, Eric
dc.contributor.authorSeip, Kristian
dc.date.accessioned2020-09-25T10:53:51Z
dc.date.available2020-09-25T10:53:51Z
dc.date.created2020-09-17T07:52:18Z
dc.date.issued2020
dc.identifier.citationFunctiones et Approximatio Commentarii Mathematici. 2020, 63 125-131.en_US
dc.identifier.issn0208-6573
dc.identifier.urihttps://hdl.handle.net/11250/2679678
dc.description.abstractWe study multiplicative functions f satisfying |f(n)|≤1 for all n, the associated Dirichlet series F(s):=∑∞n=1f(n)n−s, and the summatory function Sf(x):=∑n≤xf(n). Up to a possible trivial contribution from the numbers f(2k), F(s) may have at most one zero or one pole on the one-line, in a sense made precise by Hal\'{a}sz. We estimate logF(s) away from any such point and show that if F(s) has a zero on the one-line in the sense of Halász, then |Sf(x)|≤(x/logx)exp(cloglogx−−−−−−−√) for all c>0 when x is large enough. This bound is best possible.en_US
dc.language.isoengen_US
dc.publisherAdam Mickiewicz University, Faculty of Mathematics and Computer Scienceen_US
dc.titleA footnote to a theorem Halászen_US
dc.typeJournal articleen_US
dc.typePeer revieweden_US
dc.description.versionacceptedVersionen_US
dc.source.pagenumber125-131en_US
dc.source.volume63en_US
dc.source.journalFunctiones et Approximatio Commentarii Mathematicien_US
dc.identifier.doi10.7169/facm/1847
dc.identifier.cristin1830673
dc.relation.projectNorges forskningsråd: 275113en_US
dc.description.localcodeThis article will not be available due to copyright restrictions (c) 2020 by Adam Mickiewicz University, Faculty of Mathematics and Computer Scienceen_US
cristin.ispublishedtrue
cristin.fulltextpostprint
cristin.qualitycode1


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