On small values of the Riemann zeta-function on the critical line and gaps between zeros

Aleksandar Ivić

On small values of the Riemann zeta-function on the critical line and gaps between zeros

Number Theory 2007-05-23 v1

Authors: Aleksandar Ivić

Abstract

Small values of $|\zeta(1/2+it)|$ are investigated, using the value distribution results of A. Selberg. This gives an asymptotic formula for $\mu(\{0 < t \le T : |\zeta(1/2+it)| \le c\})$ . Some related problems involving values of $|\zeta(1/2+it)|$ and gaps between the consecutive ordinates of zeros of $\zeta(s)$ are also discussed.

Keywords

riemann zeta function critical line small values value distribution zero gaps

Cite

@article{arxiv.math/0312097,
  title  = {On small values of the Riemann zeta-function on the critical line and gaps between zeros},
  author = {Aleksandar Ivić},
  journal= {arXiv preprint arXiv:math/0312097},
  year   = {2007}
}

Comments

13 pages

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