dc.contributor.author | Saias, Eric | |
dc.contributor.author | Seip, Kristian | |
dc.date.accessioned | 2020-09-25T10:53:51Z | |
dc.date.available | 2020-09-25T10:53:51Z | |
dc.date.created | 2020-09-17T07:52:18Z | |
dc.date.issued | 2020 | |
dc.identifier.citation | Functiones et Approximatio Commentarii Mathematici. 2020, 63 125-131. | en_US |
dc.identifier.issn | 0208-6573 | |
dc.identifier.uri | https://hdl.handle.net/11250/2679678 | |
dc.description.abstract | We 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.iso | eng | en_US |
dc.publisher | Adam Mickiewicz University, Faculty of Mathematics and Computer Science | en_US |
dc.title | A footnote to a theorem Halász | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | acceptedVersion | en_US |
dc.source.pagenumber | 125-131 | en_US |
dc.source.volume | 63 | en_US |
dc.source.journal | Functiones et Approximatio Commentarii Mathematici | en_US |
dc.identifier.doi | 10.7169/facm/1847 | |
dc.identifier.cristin | 1830673 | |
dc.relation.project | Norges forskningsråd: 275113 | en_US |
dc.description.localcode | This article will not be available due to copyright restrictions (c) 2020 by Adam Mickiewicz University, Faculty of Mathematics and Computer Science | en_US |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 1 | |