Let \[ \lambda =\limsup_{\gamma}(\gamma '-\gamma)\frac{\log \gamma}{2\pi},\quad \mu =\liminf_{\gamma}(\gamma '-\gamma)\frac{\log \gamma}{2\pi} \] where \(0<\gamma \leq \gamma '\) denote the ordinates of consecutive non-trivial zeros of \(\zeta\) (s). It is expected that \(\mu =0\) and \(\lambda =\infty\), but it is known only that \(\mu <1<\lambda\). Assuming Riemann Hypothesis, H. L. Montgomery and A. M. Odlyzko [Colloq. Math. Soc. János Bolyai 34, 1079-1106 (1984; Zbl 0546.10033)] proved that \(\mu <0.5179\) and \(\lambda >1.9799.\)
In the present paper the authors assume Generalized Riemann Hypothesis and prove that \(\lambda >2.68\). They state also that, with considerable more technical details, the same result may be proved assuming only Riemann Hypothesis. The above bound for \(\lambda\) is a consequence of a mean-value formula involving the zeta-function.