Báez-Duarte, Luis New versions of the Nyman-Beurling criterion for the Riemann hypothesis. (English) Zbl 1069.11037 Int. J. Math. Math. Sci. 31, No. 7, 387-406 (2002). 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 [H. Bercovici and C. Foias, Isr. J. Math 48, 57–68 (1984; Zbl 0569.46011), M. Balazard and E. Saias, Adv. Math 139, No. 2, 310–321 (1998; Zbl 0920.11062)]. The author adds some further version of the Nyman-Beurling criterion. Reviewer: Dieter Wolke (Freiburg i. Br.) Cited in 1 Document MSC: 11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses Citations:Zbl 0065.30303; Zbl 0569.46011; Zbl 0920.11062 PDFBibTeX XMLCite \textit{L. Báez-Duarte}, Int. J. Math. Math. Sci. 31, No. 7, 387--406 (2002; Zbl 1069.11037) Full Text: DOI EuDML