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arXiv · 2405.11084

Shifting the ordinates of zeros of the Riemann zeta function

William D. Banks
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Abstract

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 \[ \zeta(\tfrac12+i\gamma)=0 \quad\text{and}\quad\zeta(\tfrac12+i(\gamma+y))\ne 0 \] hold for at least one $\gamma$ in the interval $[T,T(1+\epsilon)]$, where $\epsilon:=T^{-C/\log\log T}$.

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William D. Banks. 2024-05-17. Shifting the ordinates of zeros of the Riemann zeta function. https://arxiv.org/abs/2405.11084

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