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A Li-type criterion for zero-free half-planes of Riemann’s zeta function. (English) Zbl 1102.11046
Author’s 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 $$0< \operatorname{Re} (z) < 1$$. We study some of the properties of these functions, including their oscillatory behaviour.

##### MSC:
 11M26 Nonreal zeros of $$\zeta (s)$$ and $$L(s, \chi)$$; Riemann and other hypotheses 11M06 $$\zeta (s)$$ and $$L(s, \chi)$$
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