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

Abstract

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