A LI-TYPE CRITERION FOR ZERO-FREE HALF-PLANES OF RIEMANN’S ZETA FUNCTION

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) < 1. We study some of the properties of these functions, including their oscillatory behaviour.