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

Pedro Freitas

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

Pedro Freitas

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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 $0<\Re(z)<1$. We study some of the properties of these functions, including their oscillatory behaviour.

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Pedro Freitas. 2005-07-18. A Li-type criterion for zero-free half-planes of Riemann's zeta function. https://arxiv.org/abs/math/0507368

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