# Shifting the ordinates of zeros of the Riemann zeta function

Date: Wed, Jun 19, 2024

Location: PIMS, University of British Columbia

Conference: Comparative Prime Number Theory

Subject: Mathematics, Number Theory

Class: Scientific

CRG: L-Functions in Analytic Number Theory

### Abstract:

Let $y\neq 0$ and $C>0$. Under the Riemann Hypothesis, there is a number $T_* > 0$ (depending on $y$ and $C$) such that for every $T>T_*$, both

$$

\zeta(\frac{1}{2}+i\gamma) = 0 \qquad \mbox{and} \qquad

\zeta(\frac{1}{2} + i(\gamma + y))\neq 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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