#### Vol. 6, No. 2, 2013

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On the zeros of $\zeta(s)-c$

### Adam Boseman and Sebastian Pauli

Vol. 6 (2013), No. 2, 137–146
##### Abstract

Let $\zeta \left(s\right)$ be the Riemann zeta function and ${z}_{0}\in ℂ\setminus ℝ$ a zero of $\zeta \left(s\right)$. We investigate the graphs of the implicit functions $z:\left[0,1\right)\to ℂ$, with $z\left(0\right)={z}_{0}$ given by

$\zeta \left(z\left(c\right)\right)-c=0.$

We give zero-free regions for $\zeta \left(s\right)-c$ where $c\in \left[0,1\right)$.

##### Keywords
Riemann zeta function
Primary: 11M26