Zero-free half-planes of the \(\zeta \)-function via spaces of analytic functions (Q6594392)

In this paper under review, the authors investigate The \(H^2(\mathbb{D})\) version of Báez-Duarte's Hilbert space reformulation of the Riemann hypothesis (RH) [\textit{S. W. Noor}, Adv. Math. 350, 242--255 (2019; Zbl 1428.46020)] in a more general framework. More precisely, the authors introduce a general approach for deriving zero-free half-planes for the Riemann zeta function \(\zeta(s)\) by identifying topological vector spaces of analytic functions with specific properties. In the particular case of weighted \(\ell^2\) spaces and the classical Hardy spaces \(H^p\) \((0<p\leq 2)\) they derive precise conditions which yield zero-free half planes for the \(\zeta(s)\).