Some remarks on the differences between ordinates of consecutive zeta zeros

TL;DR

This paper investigates the differences between consecutive zeros of the Riemann zeta-function, providing results on their maximal order and sums of their powers, contributing to understanding the distribution of these zeros.

Contribution

It presents new results on the maximal gaps and sum estimates of differences between consecutive zeros of the Riemann zeta-function.

Findings

Results on the maximal order of zero differences

Estimates for sums of powers of zero gaps

Insights into the distribution of zeta zeros

Abstract

If $0 < \gamma_1 \le \gamma_2 \le \gamma_3 \le \ldots$ denote ordinates of complex zeros of the Riemann zeta-function $\zeta(s)$, then several results involving the maximal order of $\gamma_{n+1}-\gamma_n$ and the sum $$ \sum_{0<\gamma_n\le T}{(\gamma_{n+1}-\gamma_n)}^k \qquad(k>0) $$ are proved.