On Certain Spectral Operators Associated with the Riemann Zeta Function - with consequences for the Riemann Hypothesis
Year: 2025
Type: article
Abstract: This paper develops a spectral-operator framework for the Riemann zeta function, utilizing renormalized trace identities and distributional analysis to address the Hilbert-Pólya program. The authors construct a canonical "infinite-prime" self-adjoint operator through the renormalized limit of prime-weighted scaling perturbations. Unconditionally, the work establishes that the renormalized spectral distribution of this operator coincides with the nontrivial zero distribution of the Riemann zeta function. The study identifies a structural low-frequency obstruction that prevents the associated Prime Renormalized Spectral Form (PRSF) from being coercive on the full Hilbert space. Consequently, the Riemann Hypothesis is reformulated as a rigidity principle: it is equivalent to the existence of a unique, canonical admissible boundary condition that restores coercivity to the PRSF.
Author: Botha, Marius
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7116307261
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