English

A Li-type criterion for zero-free half-planes of Riemann's zeta function

Number Theory 2007-05-23 v1

Abstract

We define a sequence of real functions which coincide with Li's coefficients at one and which allow us to extend Li's criterion for the Riemann Hypothesis to yield a necessary and sufficient condition for the existence of zero-free strips inside the critical strip 0<(z)<10<\Re(z)<1. We study some of the properties of these functions, including their oscillatory behaviour.

Keywords

Cite

@article{arxiv.math/0507368,
  title  = {A Li-type criterion for zero-free half-planes of Riemann's zeta function},
  author = {Pedro Freitas},
  journal= {arXiv preprint arXiv:math/0507368},
  year   = {2007}
}

Comments

15 pages, to appear in the J. London Math. Soc