New versions of the Nyman-Beurling criterion for the Riemann hypothesis
The paper contains a detailed discussion of the Nyman-Beurling criterion for the truth of the quasi-Riemann hypothesis. \[ \zeta(s)\neq 0 \quad\text{for}\quad\sigma=\text{Re}\,s>\frac 1p \] for some \(p\in (1, \infty)\) [Proc. Natl. Acad. Sci. USA 41, 312--314 (1955; Zbl 0065.30303)]. There exist several extensions of the original statement [\textit{H. Bercovici} and \textit{C. Foias}, Isr. J. Math 48, 57--68 (1984; Zbl 0569.46011), \textit{M. Balazard} and \textit{E. Saias}, Adv. Math 139, No. 2, 310--321 (1998; Zbl 0920.11062)]. The author adds some further version of the Nyman-Beurling criterion.
scientific article; zbMATH DE number 1796602