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

D. A. Goldston; S. M. Gonek

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

Number Theory 2007-05-23 v1

Authors: D. A. Goldston , S. M. Gonek

Abstract

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.

Keywords

Riemann zeta-function argument of zeta-function Riemann Hypothesis S(t) bounds zeros multiplicity zero gaps

Cite

@article{arxiv.math/0511092,
  title  = {A note on S(T) and the zeros of the Riemann zeta-function},
  author = {D. A. Goldston and S. M. Gonek},
  journal= {arXiv preprint arXiv:math/0511092},
  year   = {2007}
}

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5 pages

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

Abstract

Keywords

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