Large gaps between consecutive zeros, on the critical line, of the Riemann zeta-function

We show that for any sufficiently large $T,$ there exists a subinterval of $[T,2T]$ of length at least $2.766\times \frac{2\pi }{\log T},$ in which the function $t\mapsto \zeta (1\mathrm{/}2+it)$ has no zeros.