Let $\gamma$ denote the imaginary part of a non-trivial zero of the Riemann zeta function. Do there exist some function $f$ such that $\gamma\_{n+1} - \gamma\_n > f(n)>0$ for all large $n$? To be more explicit, do there exist some $c > 1$ such that $\gamma\_{n+1}-\gamma\_n > n^{-c}$ for all $n>n\_0$ ?



On gaps between consecutive zeros of the Riemann zeta function
Your first question can be reformulated as follows: [Are the nontrivial zeros of the Riemann zeta simple?](https://mathoverflow.net/questions/59770/are-the-nontrivial-zeros-of-the-riemann-zeta-simple) We don't know the answer to that question, even under the Riemann hypothesis.


