A modest improvement on the function $S(T)$

preprint2010arXivOpen access

This paper contains a small improvement to the explicit bounds on the growth of the function $S(T)$ . It is shown how more substantial improvements are possible if one has better explicit bounds on the growth of $|ζ(\frac{1}{2}+it)|$ .

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A modest improvement on the function $S(T)$

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A modest improvement on the function S(T)S(T)S(T)

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A modest improvement on the function $S(T)$