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

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

2005-11-03

arxiv.org/abs/math/0511092v1

Mathematics

Number Theory

5 pages

Scientific paper

Let $\pi S(t)$ 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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