Shifting the ordinates of zeros of the Riemann zeta function
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917803184881664 |
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| author | Banks, William D. |
| author_facet | Banks, William D. |
| contents | Let $y\ne 0$ and $C>0$. Under the Riemann Hypothesis, there is a number $T_*>0$ $($depending on $y$ and $C)$ such that for every $T\ge T_*$, both \[ ζ(\tfrac12+iγ)=0 \quad\text{and}\quadζ(\tfrac12+i(γ+y))\ne 0 \] hold for at least one $γ$ in the interval $[T,T(1+ε)]$, where $ε:=T^{-C/\log\log T}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11084 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shifting the ordinates of zeros of the Riemann zeta function Banks, William D. Number Theory 11M26, 11M06 Let $y\ne 0$ and $C>0$. Under the Riemann Hypothesis, there is a number $T_*>0$ $($depending on $y$ and $C)$ such that for every $T\ge T_*$, both \[ ζ(\tfrac12+iγ)=0 \quad\text{and}\quadζ(\tfrac12+i(γ+y))\ne 0 \] hold for at least one $γ$ in the interval $[T,T(1+ε)]$, where $ε:=T^{-C/\log\log T}$. |
| title | Shifting the ordinates of zeros of the Riemann zeta function |
| topic | Number Theory 11M26, 11M06 |
| url | https://arxiv.org/abs/2405.11084 |