Report
A Hardy-space operator acting on $ζ$-zeros
| Τίτλος: | A Hardy-space operator acting on $ζ$-zeros |
|---|---|
| Συγγραφείς: | Manzur, Juan, Noor, Waleed |
| Έτος έκδοσης: | 2026 |
| Θεματικοί όροι: | Functional Analysis, 11M26, 47A15, 30H10 |
| Περιγραφή: | 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. 7 pages |
| Τύπος εγγράφου: | Working Paper |
| DOI: | 10.48550/arXiv.2610.03568 |
| Σύνδεσμος πρόσβασης: | https://arxiv.org/abs/2610.03568 |
| Αριθμός Καταχώρησης: | edsarx.2610.03568 |
| Βάση Δεδομένων: | arXiv |
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