Large gaps between consecutive zeros of the Riemann zeta-function. II

TL;DR

Under the assumption of the Riemann Hypothesis, the paper proves that there are infinitely many pairs of consecutive zeros of the Riemann zeta-function with gaps significantly larger than the average spacing, specifically exceeding 2.9 times the average.

Contribution

The paper establishes the existence of infinitely many large gaps between zeros of the Riemann zeta-function under the Riemann Hypothesis, advancing understanding of zero distribution.

Findings

Existence of infinitely many large gaps > 2.9 times average

Conditional proof assuming Riemann Hypothesis

Improves previous bounds on zero gaps

Abstract

Assuming the Riemann Hypothesis we show that there exist infinitely many consecutive zeros of the Riemann zeta-function whose gaps are greater than 2.9 times the average spacing.