Selberg's conjecture concerning the distribution of imaginary parts of zeros of the Riemann zeta function (Q542218)

Let \(\gamma_n\) denote the positive ordinates of zeros of the Riemann zeta function arranged in increasing order, \(t_n\) the Gramm points, \(\Delta_n=n-\nu\) with \(t_{\nu-1}<\gamma_n\leq t_\nu\). The author proves Selberg's conjecture: if \(\Phi(n)\) is a positive function of \(n\) tending to \(\infty\) then \[ \frac{\sqrt{\log\log n}}{\Phi(n)}<|\Delta_n|<\Phi(n)\sqrt{\log\log n} \] for almost all \(n\).