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

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.

13 pages