A Unitary Scattering Perspective on the Riemann Hypothesis
Year: 2026
Type: article
Abstract: We construct an arithmetic scattering model over the multiplicative semigroup of prime numbers, following the Hilbert–Pólya programme. The nontrivial zeros of the Riemann zeta function are interpreted as resonance poles of a unitary scattering operator defined on a Hilbert space built from prime orbits. Under the core spectral and unitarity assumptions of the model, all nontrivial zeros are constrained to lie on the critical line $\mathrm{Re}(s)=1/2$. This work is a conditional argument, not an unconditional mathematical proof of the Riemann hypothesis.
Author: Chen, H.P.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225620731
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