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arXiv · 2610.03568

A Hardy-space operator acting on $ζ$-zeros

Juan Manzur·Waleed Noor
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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.

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Juan Manzur, Waleed Noor. 2026-10-02. A Hardy-space operator acting on $ζ$-zeros. https://arxiv.org/abs/2610.03568

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