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dc.contributor.authorLamzouri, Yen_US
dc.contributor.authorLESTER, SJen_US
dc.contributor.authorRadziwill, Men_US
dc.date.accessioned2017-09-01T14:42:49Z
dc.date.available2017-08-05en_US
dc.date.issued2018-11-20en_US
dc.date.submitted2017-08-22T14:36:13.972Z
dc.identifier.issn1420-8946en_US
dc.identifier.urihttp://qmro.qmul.ac.uk/xmlui/handle/123456789/25579
dc.description.abstractLet 0<r<1/4, and f be a non-vanishing continuous function in |z|≤r, that is analytic in the interior. Voronin’s universality theorem asserts that translates of the Riemann zeta function ζ(3/4+z+it) can approximate f uniformly in |z|<r to any given precision ε, and moreover that the set of such t∈[0,T] has measure at least c(ε)T for some c(ε)>0, once T is large enough. This was refined by Bagchi who showed that the measure of such t∈[0,T] is (c(ε)+o(1))T, for all but at most countably many ε>0. Using a completely different approach, we obtain the first effective version of Voronin's Theorem, by showing that in the rate of convergence one can save a small power of the logarithm of T. Our method is flexible, and can be generalized to other L-functions in the t-aspect, as well as to families of L-functions in the conductor aspect.en_US
dc.format.extent709 - 736en_US
dc.languageEnglishen_US
dc.publisherEuropean Mathematical Societyen_US
dc.relation.ispartofCommentarii Mathematici Helveticien_US
dc.rightsThis is a pre-copyedited, author-produced version of an article accepted for publication in Commentarii Mathematici Helvetici following peer review
dc.subjectRiemann zeta functionen_US
dc.subjectuniversalityen_US
dc.titleAn effective universality theorem for the Riemann zeta functionen_US
dc.typeArticle
dc.rights.holder© 2017 European Mathematical Society
dc.identifier.doi10.4171/CMH/448en_US
pubs.issue4en_US
pubs.notesNot knownen_US
pubs.publication-statusPublisheden_US
pubs.publisher-urlhttps://www.ems-ph.org/journals/show_issue.php?issn=0010-2571&vol=93&iss=4en_US
pubs.volume93en_US
dcterms.dateAccepted2017-08-05en_US


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