Involve: A Journal of Mathematics

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

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

Adam Boseman and Sebastian Pauli

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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).

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513733571

Digital Object Identifier
doi:10.2140/involve.2013.6.137

Mathematical Reviews number (MathSciNet)
MR3096365

Zentralblatt MATH identifier
1291.11117

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

Keywords
Riemann zeta function

Citation

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. https://projecteuclid.org/euclid.involve/1513733571


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References

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