A Li-type criterion for zero-free half-planes of Riemann’s zeta function. (English) Zbl 1102.11046

Freitas, Pedro

J. Lond. Math. Soc., II. Ser. 73, No. 2, 399-414 (2006).

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.

Reviewer: Tianze Wang (Henan)

MSC:

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

Keywords:

Riemann zeta function; Riemann Hypothesis; Li’s coefficients; zero-free half-plane