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On an inequality for the Riemann zeta-function in the critical strip

Classical Analysis and ODEs 2012-06-11 v1 Number Theory

Authors: Sadegh Nazardonyavi , Semyon Yakubovich

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Abstract

By using new power inequalities we give an elementary proof of an important relation for the Riemann zeta-function |\zeta(1-s)| <= |\zeta(s)| in the strip 0< Re s<1/2,\ |\Im s| >= 12. Moreover, we establish a sufficient condition of the validity of the Riemann hypothesis in terms of the derivative with respect to Re s of |\zeta(s)|^2 and conjecture its necessity.

Keywords

Riemann zeta-function inequality critical strip Riemann hypothesis elementary proof derivative

Cite

@article{arxiv.1206.1801,
  title  = {On an inequality for the Riemann zeta-function in the critical strip},
  author = {Sadegh Nazardonyavi and Semyon Yakubovich},
  journal= {arXiv preprint arXiv:1206.1801},
  year   = {2012}
}