A note on the gaps between consecutive zeros of the Riemann zeta-function

TL;DR

Under the assumption of the Riemann Hypothesis, the paper establishes bounds on the gaps between consecutive non-trivial zeros of the Riemann zeta-function, showing they can be both significantly smaller and larger than the average spacing.

Contribution

The paper provides new bounds on the size of gaps between zeros of the Riemann zeta-function assuming the Riemann Hypothesis, highlighting the variability in zero spacing.

Findings

Gaps can be at most 0.5155 times the average spacing

Gaps can be at least 2.69 times the average spacing

Infinitely many zeros exhibit these extreme gaps

Abstract

Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.5155 times the average spacing and infinitely often they differ by at least 2.69 times the average spacing.