An Escalator Model of the Riemann Zeta Function, with a Note on the Truncated Photon
This paper offers a visual model of the Riemann zeta function written by an independent thinker rather than a professional mathematician. The function is pictured as an escalator. Its top landing is the region where the primes build the function; its bottom landing holds the evenly spaced trivial zeros; and between them runs a belt along the line Re(s) = 12 carrying the non-trivial zeros upward forever. Each part of the picture is matched to an established result: the Euler product, the functional equation and its mirror line at 1 2, the zero-free edges behind the PrimeNumber Theorem, the explicit formula linking zeros to primes, the statistical repulsion between neighbouring zeros, and the de Bruijn–Newman constant, which describes how zeros could leave the line only by colliding and separating in mirrored pairs. The model is then tested on the first1,000 non-trivial zeros, measured using only its own properties: every step is centred and unique,the steps crowd smoothly, the system stays balanced, and a steady squeeze-and-release pulse appears in every block. The model does not prove the Riemann Hypothesis. Its purpose is to make the shape of the problem visible to non-specialists, and to record a qualitative resemblance to a recent quantum-optics result on truncated photons
Authors
- Nicolas Antony Brown (ORCID: https://orcid.org/0009-0008-6859-1640)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-11-03
- DOI
- https://doi.org/10.5281/zenodo.23927521
- Primary Topic
- Analytic Number Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00