An improved explicit bound on |ζ(12+it)|

D. J. Platt; T. S. Trudgian

doi:10.1016/j.jnt.2014.08.019

An improved explicit bound on |ζ(12+it)|

D. J. Platt, T. S. Trudgian^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

27 Citations (Scopus)

Abstract

This article proves the bound |ζ(12+it)|≤0.732t16log t for t≥. 2, which improves on a result by Cheng and Graham. We also show that |ζ(12+it)|≤0.732|4.678+it|16log |4.678+it| for all t.

Original language	English
Pages (from-to)	842-851
Number of pages	10
Journal	Journal of Number Theory
Volume	147
DOIs	https://doi.org/10.1016/j.jnt.2014.08.019
Publication status	Published - 1 Feb 2015

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title = "An improved explicit bound on |ζ(12+it)|",

abstract = "This article proves the bound |ζ(12+it)|≤0.732t16log t for t≥. 2, which improves on a result by Cheng and Graham. We also show that |ζ(12+it)|≤0.732|4.678+it|16log |4.678+it| for all t.",

keywords = "Explicit bounds, Exponential sums, Riemann zeta-function",

author = "Platt, {D. J.} and Trudgian, {T. S.}",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

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AU - Platt, D. J.

AU - Trudgian, T. S.

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N2 - This article proves the bound |ζ(12+it)|≤0.732t16log t for t≥. 2, which improves on a result by Cheng and Graham. We also show that |ζ(12+it)|≤0.732|4.678+it|16log |4.678+it| for all t.

AB - This article proves the bound |ζ(12+it)|≤0.732t16log t for t≥. 2, which improves on a result by Cheng and Graham. We also show that |ζ(12+it)|≤0.732|4.678+it|16log |4.678+it| for all t.

KW - Explicit bounds

KW - Exponential sums

KW - Riemann zeta-function

UR - http://www.scopus.com/inward/record.url?scp=84910030142&partnerID=8YFLogxK

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DO - 10.1016/j.jnt.2014.08.019

M3 - Article

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VL - 147

SP - 842

EP - 851

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

An improved explicit bound on |ζ(12+it)|

Abstract

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