dc.contributor.author | Bondarenko, Andrii | |
dc.contributor.author | Seip, Kristian | |
dc.date.accessioned | 2019-02-19T11:40:53Z | |
dc.date.available | 2019-02-19T11:40:53Z | |
dc.date.created | 2018-11-27T14:55:47Z | |
dc.date.issued | 2018 | |
dc.identifier.citation | Mathematische Annalen. 2018, 372 999-2015. | nb_NO |
dc.identifier.issn | 0025-5831 | |
dc.identifier.uri | http://hdl.handle.net/11250/2586218 | |
dc.description.abstract | We combine our version of the resonance method with certain convolution formulas for ζ(s) and logζ(s) . This leads to a new Ω result for |ζ(1/2+it)| : The maximum of |ζ(1/2+it)| on the interval 1≤t≤T is at least exp((1+o(1))logTlogloglogT/loglogT−−−−−−−−−−−−−−−−−−−−−√) . We also obtain conditional results for S(t):=1/π times the argument of ζ(1/2+it) and S1(t):=∫t0S(τ)dτ . On the Riemann hypothesis, the maximum of |S(t)| is at least clogTlogloglogT/loglogT−−−−−−−−−−−−−−−−−−−−−√ and the maximum of S1(t) is at least c1logTlogloglogT/(loglogT)3−−−−−−−−−−−−−−−−−−−−−−−√ on the interval Tβ≤t≤T whenever 0≤β<1 . | nb_NO |
dc.language.iso | eng | nb_NO |
dc.publisher | Springer Verlag | nb_NO |
dc.title | Extreme values of the Riemann zeta function and its argument | nb_NO |
dc.title.alternative | Extreme values of the Riemann zeta function and its argument | nb_NO |
dc.type | Journal article | nb_NO |
dc.type | Peer reviewed | nb_NO |
dc.description.version | acceptedVersion | nb_NO |
dc.source.pagenumber | 999-2015 | nb_NO |
dc.source.volume | 372 | nb_NO |
dc.source.journal | Mathematische Annalen | nb_NO |
dc.identifier.doi | 10.1007/s00208-018-1663-2 | |
dc.identifier.cristin | 1635879 | |
dc.relation.project | Norges forskningsråd: 275113 | nb_NO |
dc.description.localcode | This is a post-peer-review, pre-copyedit version of an article published in [Mathematische Annalen] Locked until 6.3.2019 due to copyright restrictions. The final authenticated version is available online at: https://doi.org/10.1007/s00208-018-1663-2 | nb_NO |
cristin.unitcode | 194,63,15,0 | |
cristin.unitname | Institutt for matematiske fag | |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 2 | |