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

2003/12/04 by Aleksandar Ivić
Mathematics · #math.NT #msc:11M06

paper · pdf

published as Lietuvos Matem. Rinkinys 42(2002), 31-45 · 13 pages

arxiv created 2003/12/04 · arxiv updated 2009/12/01

Abstract

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

Related

• The a-values of the Riemann zeta function near the critical line
• A new approach to gaps between zeta zeros
• Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function
• Gaps between zeros of the Riemann zeta-function
• Large gaps between consecutive zeros, on the critical line, of the Riemann zeta-function