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 ζ(s) be the Riemann zeta function and z0 a zero of ζ(s). We investigate the graphs of the implicit functions z : [0,1) , with z(0) = z0 given by

ζ(z(c)) c = 0.

We give zero-free regions for ζ(s) c where c [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