The explicit upper bound of the multiple integral of $S(t)$ on the Riemann Hypothesis

Takahiro Wakasa

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arXiv · 1210.3097

The explicit upper bound of the multiple integral of $S(t)$ on the Riemann Hypothesis

Takahiro Wakasa

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Abstract

We prove explicit upper bounds of the function $S_m(T)$, defined by the repeated integration of the argument of the Riemann zeta-function. The explicit upper bound of $S(T)$ and $S_1(T)$ have already been obtained by A. Fujii. Our result is a generalization of Fujii's results.

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Takahiro Wakasa. 2012-10-11. The explicit upper bound of the multiple integral of $S(t)$ on the Riemann Hypothesis. https://arxiv.org/abs/1210.3097

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