Unconditional Bounds for Two, Three and Four Consecutive Moderate Gaps between Zeros of the Riemann Zeta Function

César Angón; Erick Ross; Ze Sen Tang; Boyang Zhao

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arXiv · 2610.22927

Unconditional Bounds for Two, Three and Four Consecutive Moderate Gaps between Zeros of the Riemann Zeta Function

César Angón·Erick Ross·Ze Sen Tang·Boyang Zhao

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Abstract

We prove unconditional positive-proportion results for consecutive moderate gaps between zeros of the Riemann zeta function. More precisely, for every fixed $0 0$. The proof combines Lamzouri's Hilbert-space formulation of the Montgomery--Taylor second-moment method with local spectral estimates for simple critical-line zeros and a cluster-counting argument that accounts for multiple zeros and zeros off the critical line.

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BibTeX RIS

César Angón, Erick Ross, Ze Sen Tang, Boyang Zhao. 2026-10-16. Unconditional Bounds for Two, Three and Four Consecutive Moderate Gaps between Zeros of the Riemann Zeta Function. https://arxiv.org/abs/2610.22927

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