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A note on S(T) and the zeros of the Riemann zeta-function

D. A. Goldston·S. M. Gonek
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Abstract

Let $πS(t)$ denote the argument of the Riemann zeta-function at the point $\frac12+it$. Assuming the Riemann Hypothesis, we sharpen the constant in the best currently known bounds for $S(t)$ and for the change of $S(t)$ in intervals. We then deduce estimates for the largest multiplicity of a zero of the zeta-function and for the largest gap between the zeros.

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D. A. Goldston, S. M. Gonek. 2005-11-03. A note on S(T) and the zeros of the Riemann zeta-function. https://arxiv.org/abs/math/0511092

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