The Prime Frequency Calculus: A Signal Processing Perspective on Riemann's 1859 Memoir
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This article summarizes the "Fourier-like" interpretation of Bernhard Riemann's 1859 paper. By treating the distribution of prime numbers as a discrete impulse train in the time domain and the Riemann Zeta function as a frequency-domain transform, we demonstrate that the Prime Number Theorem and the Riemann Hypothesis are essentially statements regarding signal stability and optimal sampling conditions.
Fields of Study & Subjects
Analytic Number Theory Research
Mathematical Analysis and Transform Methods
Mathematical and Theoretical Analysis
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 16 March 2026
- Language
- EN
- Document type
- Preprint