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

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.