Mathematics > Number Theory
[Submitted on 17 May 2024 (v1), last revised 15 Oct 2024 (this version, v2)]
Title:Shifting the ordinates of zeros of the Riemann zeta function
View PDF HTML (experimental)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 $\epsilon:=T^{-C/\log\log T}$.
Submission history
From: William Banks [view email][v1] Fri, 17 May 2024 20:34:32 UTC (13 KB)
[v2] Tue, 15 Oct 2024 13:39:53 UTC (15 KB)
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