Consecutive moderate gaps between zeros of the Riemann zeta function

Abstract

Let $0<{\hat{I}}_1^3\le {\hat{I}}_2^3\le \cdots$ denote the ordinates of nontrivial zeros of the Riemann zeta function with positive imaginary parts. For $c>0$ fixed (but possibly small), $T$ large, and ${\hat{I}}_n^3\le T$, we call a gap ${\hat{I}}_{n+1}^3-{\hat{I}}_n^3$ between consecutive ordinates ``moderate'' if ${\hat{I}}_{n+1}^3-{\hat{I}}_n^3\ge 2\ddot{I}€c/\log T$. We investigate whether infinitely often there exists $r$ consecutive moderate gaps between ordinates ${\hat{I}}_{n+1}^3-{\hat{I}}_n^3,{\hat{I}}_{n+2}^3-{\hat{I}}_{n+1}^3,\dots ,{\hat{I}}_{n+r}^3-{\hat{I}}_{n+r-1}^3$.

13 pages, 14 references; comments are welcome!