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 . 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