Consecutive moderate gaps between zeros of the Riemann zeta function
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912162801254400 |
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| author | Gonek, Steven M. Sahay, Anurag |
| author_facet | Gonek, Steven M. Sahay, Anurag |
| contents | Let $0<γ_1\leq γ_2 \leq \cdots $ denote the ordinates of nontrivial zeros of the Riemann zeta function with positive imaginary parts.
For $c>0$ fixed (but possibly small), $T$ large, and $γ_n\leq T$, we call a gap $γ_{n+1}-γ_n$ between consecutive ordinates ``moderate'' if $γ_{n+1}-γ_n \geq 2πc/\log T$. We investigate whether infinitely often there exists $r$ consecutive moderate gaps between ordinates $γ_{n+1}-γ_n, γ_{n+2}-γ_{n+1}, \ldots , γ_{n+r}- γ_{n+r-1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15481 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Consecutive moderate gaps between zeros of the Riemann zeta function Gonek, Steven M. Sahay, Anurag Number Theory 11M06, 11M26 Let $0<γ_1\leq γ_2 \leq \cdots $ denote the ordinates of nontrivial zeros of the Riemann zeta function with positive imaginary parts. For $c>0$ fixed (but possibly small), $T$ large, and $γ_n\leq T$, we call a gap $γ_{n+1}-γ_n$ between consecutive ordinates ``moderate'' if $γ_{n+1}-γ_n \geq 2πc/\log T$. We investigate whether infinitely often there exists $r$ consecutive moderate gaps between ordinates $γ_{n+1}-γ_n, γ_{n+2}-γ_{n+1}, \ldots , γ_{n+r}- γ_{n+r-1}$. |
| title | Consecutive moderate gaps between zeros of the Riemann zeta function |
| topic | Number Theory 11M06, 11M26 |
| url | https://arxiv.org/abs/2412.15481 |