Small gaps between consecutive zeros of the Riemann zeta-function

Shōta Inoue

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arXiv · 2604.05733

Small gaps between consecutive zeros of the Riemann zeta-function

Shōta Inoue

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Abstract

In this paper, we introduce the resonance-correlation method to study small gaps between consecutive zeros of the Riemann zeta-function. Our method is based on a synthesis of Montgomery's pair correlation approach and the Montgomery-Odlyzko method. As an application, we break the persistent practical barrier around $0.515$ and prove $\mu < 0.50895$ under the Riemann Hypothesis.

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Shōta Inoue. 2026-04-07. Small gaps between consecutive zeros of the Riemann zeta-function. https://arxiv.org/abs/2604.05733

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