The Prime Signal Sieve
Abstract
This technical note examines the Riemann Hypothesis through the lens of Prime Gear Geometry (PGG) and Digital Signal Processing (DSP). We posit that Riemann's $\xi(t)$ function is not merely a mathematical curiosity but the world’s first frequency-domain Prime Signal Sieve. By interpreting the adjective ``real'' as ``authentic/functional,'' we demonstrate that the distribution of primes is the deterministic output of a lossless mechanical engine centered on the Fourier bridge.
Fields of Study & Subjects
Analytic Number Theory Research
Mathematical Analysis and Transform Methods
Advanced Mathematical Theories and Applications
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 12 March 2026
- Language
- EN
- Document type
- Preprint