×

zbMATH — the first resource for mathematics

A Li-type criterion for zero-free half-planes of Riemann’s zeta function. (English) Zbl 1102.11046
Author’s 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 \(0< \operatorname{Re} (z) < 1\). We study some of the properties of these functions, including their oscillatory behaviour.

MSC:
11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
PDF BibTeX XML Cite
Full Text: DOI arXiv