A Li-type criterion for zero-free half-planes of Riemann's zeta function
Abstract
Description
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 $0<\Re(z)<1$. We study some of the properties of these functions, including their oscillatory behaviour.
15 pages, to appear in the J. London Math. Soc
15 pages, to appear in the J. London Math. Soc