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

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

2005-07-18

arxiv.org/abs/math/0507368v1

Mathematics

Number Theory

15 pages, to appear in the J. London Math. Soc

Scientific paper

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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