A new upper bound for ζ(1+ it)

Timothy Trudgian

doi:10.1017/S0004972713000415

A new upper bound for ζ(1+ it)

Timothy Trudgian^*

^*Corresponding author for this work

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

9 Citations (Scopus)

Abstract

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}.

Original language	English
Pages (from-to)	259-264
Number of pages	6
Journal	Bulletin of the Australian Mathematical Society
Volume	89
Issue number	2
DOIs	https://doi.org/10.1017/S0004972713000415
Publication status	Published - Apr 2014

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title = "A new upper bound for ζ(1+ it)",

abstract = "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 {\.2} 105.",

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author = "Timothy Trudgian",

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AB - 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.

KW - Riemann zeta-function

KW - critical strip

KW - exponential sums

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DO - 10.1017/S0004972713000415

M3 - Article

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VL - 89

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EP - 264

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 2

ER -

A new upper bound for ζ(1+ it)

Abstract

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