Involve: A Journal of Mathematics

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  • Volume 6, Number 2 (2013), 137-146.

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

Adam Boseman and Sebastian Pauli

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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).

Article information

Involve, Volume 6, Number 2 (2013), 137-146.

Received: 8 March 2012
Revised: 31 May 2012
Accepted: 15 May 2013
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11M26: Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses

Riemann zeta function


Boseman, Adam; Pauli, Sebastian. On the zeros of $\zeta(s)-c$. Involve 6 (2013), no. 2, 137--146. doi:10.2140/involve.2013.6.137.

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