On the zeros of ζ(s) − c

Boseman, Adam; Pauli, Sebastian

doi:10.2140/involve.2013.6.137

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

Adam Boseman and Sebastian Pauli

Vol. 6 (2013), No. 2, 137–146

DOI: 10.2140/involve.2013.6.137

Abstract

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

ζ (z (c)) - c = 0 .

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

Keywords

Riemann zeta function

Mathematical Subject Classification 2010

Primary: 11M26

Milestones

Received: 8 March 2012

Revised: 31 May 2012

Accepted: 15 May 2013

Published: 1 September 2013

Communicated by Filip Saidak

Authors

Adam Boseman
Joint School of Nanoscience and Nanoengineering The University of North Carolina at Greensboro Greensboro, North Carolina 27402 United States

Sebastian Pauli
Department of Mathematics and Statistics The University of North Carolina at Greensboro Greensboro, North Carolina 27402 United States

Vol. 6, No. 2, 2013