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arXiv:1208.5846 [math.NT]AbstractReferencesReviewsResources

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

T. S. Trudgian

Published 2012-08-29, updated 2012-09-05Version 2

This paper improves the bound on $|S(T)|$. The main result is to show that $|S(T)|\leq 0.111\log T + 0.275\log\log T + 2.450$, which is valid for all $T\geq e$.

Comments: 10 pages, two tables: this is the second version of this article in which I have made some minor alterations and corrections
Journal: 2014, J. Number Theory, vol. 134, pp. 280-292
Categories: math.NT
Subjects: 11M06, 11M26
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