An improved upper bound for the argument of the Riemann zeta-function on the critical line II

Timothy S. Trudgian

doi:10.1016/j.jnt.2013.07.017

An improved upper bound for the argument of the Riemann zeta-function on the critical line II

Timothy S. Trudgian^*

^*Corresponding author for this work

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

44 Citations (Scopus)

Abstract

Text: This paper concerns the function S(. T), where π. S(. T) is the argument of the Riemann zeta-function along the critical line. The main result is that. |S(T)|≤0.112logT+0.278loglogT+2.510, which holds for all T ≥ e. Video: For a video summary of this paper, please click here or visit http://youtu.be/FldP0idE0aI.

Original language	English
Pages (from-to)	280-292
Number of pages	13
Journal	Journal of Number Theory
Volume	134
DOIs	https://doi.org/10.1016/j.jnt.2013.07.017
Publication status	Published - Jan 2014

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abstract = "Text: This paper concerns the function S(. T), where π. S(. T) is the argument of the Riemann zeta-function along the critical line. The main result is that. |S(T)|≤0.112logT+0.278loglogT+2.510, which holds for all T ≥ e. Video: For a video summary of this paper, please click here or visit http://youtu.be/FldP0idE0aI.",

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AB - Text: This paper concerns the function S(. T), where π. S(. T) is the argument of the Riemann zeta-function along the critical line. The main result is that. |S(T)|≤0.112logT+0.278loglogT+2.510, which holds for all T ≥ e. Video: For a video summary of this paper, please click here or visit http://youtu.be/FldP0idE0aI.

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KW - Riemann zeta-function

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JO - Journal of Number Theory

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ER -

An improved upper bound for the argument of the Riemann zeta-function on the critical line II

Abstract

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