On gaps between zeros of the Riemann zeta function

TL;DR

Under the assumption of the Riemann Hypothesis, the paper proves that the gaps between consecutive non-trivial zeros of the Riemann zeta-function vary infinitely often, being both significantly larger and smaller than the average spacing.

Contribution

It establishes new bounds on the size of gaps between zeros of the Riemann zeta-function assuming the Riemann Hypothesis.

Findings

Gaps can be at least 2.7327 times the average spacing.

Gaps can be at most 0.5154 times the average spacing.

Results hold infinitely often under the Riemann Hypothesis.

Abstract

Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at least 2.7327 times the average spacing and infinitely often they differ by at most 0.5154 times the average spacing.