Small gaps between consecutive zeros of the Riemann zeta-function
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915920556851200 |
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| author | Inoue, Shōta |
| author_facet | Inoue, Shōta |
| contents | 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 $μ< 0.50895$ under the Riemann Hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05733 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Small gaps between consecutive zeros of the Riemann zeta-function Inoue, Shōta Number Theory 11M26, 11M06 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 $μ< 0.50895$ under the Riemann Hypothesis. |
| title | Small gaps between consecutive zeros of the Riemann zeta-function |
| topic | Number Theory 11M26, 11M06 |
| url | https://arxiv.org/abs/2604.05733 |