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

Abstract

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

arXiv comment10 pages, two tables: this is the second version of this article in which I have made some minor alterations and corrections

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