Year: 2026
Type: preprint
Abstract: A Hardy space approach to the Nyman-Beurling and Báez-Duarte criterion for the Riemann Hypothesis (RH) was introduced in [7]. It states that the RH holds if and only if the span of a particular sequence of functions $(h_k)_{k\geq2}$, denoted $\mathcal{N}$, is dense in the Hardy space $H^2$. In this note we construct a bounded operator $T$ on $H^{2}$ such that if the closure of $\mathcal{N}$ is $T$-invariant, then either the RH holds or there exists an infinite progression of $ζ$-zeros. In particular, this yields an operator-theoretic criterion for the Riemann hypothesis as an invariant subspace question.
Source: arXiv (Cornell University)
Authors: Manzur, Juan, Noor, Waleed
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220363181