On $r$-gaps between zeros of the Riemann zeta-function

J. B. Conrey, C. L. Turnage-Butterbaugh

Under the Riemann Hypothesis, we prove for any natural number $r$ there exist infinitely many large natural numbers $n$ such that $({\gamma }_{n+r}-{\gamma }_n)/(2\pi /\log {\gamma }_n)>r+\Theta \sqrt{r}$ and…