On large distances between consecutive zeros of the Riemann zeta-function

We obtain a new estimate for the number of zeros $\rho_n=\beta_n+i\gamma_n$ of the Riemann zeta-function, $14<\gamma_1<\gamma_2<\dots\le\gamma_n\le\gamma_{n+1}\le\cdots$, whose ordinates $\gamma_n$ belong to a given interval and for which the difference $\gamma_{n+r}-\gamma_n$ is sufficiently large in comparison with the ‘mean’ value $2\pi r(\ln\frac{\gamma_n}{2\pi})^{-1}$.