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A new upper bound for |ζ(1+it)|

Trudgian, Timothy

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It is known that ζ(1+ it)<(log t)2/3 when t> 1. This paper provides a new explicit estimate ζ(1+ it) ≤ 3/4 log t, for t≥ 3. This gives the best upper bound on ζ (1+ it) for t≤ 10 2̇ 105.

dc.contributor.authorTrudgian, Timothy
dc.date.accessioned2015-12-07T22:25:10Z
dc.identifier.issn0004-9727
dc.identifier.urihttp://hdl.handle.net/1885/21141
dc.description.abstractIt is known that ζ(1+ it)<(log t)2/3 when t> 1. This paper provides a new explicit estimate ζ(1+ it) ≤ 3/4 log t, for t≥ 3. This gives the best upper bound on ζ (1+ it) for t≤ 10 2̇ 105.
dc.publisherAustralian Mathematics Publishing Association
dc.sourceBulletin of the Australian Mathematical Society
dc.titleA new upper bound for |ζ(1+it)|
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume89
dc.date.issued2014
local.identifier.absfor010101 - Algebra and Number Theory
local.identifier.ariespublicationu5328909xPUB15
local.type.statusPublished Version
local.contributor.affiliationTrudgian, Timothy, College of Physical and Mathematical Sciences, ANU
local.bibliographicCitation.issue2
local.bibliographicCitation.startpage259
local.bibliographicCitation.lastpage264
local.identifier.doi10.1017/S0004972713000415
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
dc.date.updated2015-12-07T09:32:35Z
local.identifier.scopusID2-s2.0-84902188836
local.identifier.thomsonID000338416700010
CollectionsANU Research Publications

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