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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75825We 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 $0<\Re(z)<1$. We study some of the properties of these functions, including their oscillatory behaviour.15 pages, to appear in the J. London Math. SocNumber Theory11M26; 11M06A Li-type criterion for zero-free half-planes of Riemann's zeta functiontext