Spectral Rigidity and the Explicit Formula - An RMT Perspective on Arithmetic Reconstruction
Abstract
The explicit formulas of Riemann and von Mangoldt connect the distribution of prime numbers to the zeros of the Riemann zeta function. While this duality is well-known, the mechanism by which the oscillatory sum of zeros converges to a stable arithmetic signal remains non-trivial from a spectral analysis perspective.
Fields of Study & Subjects
Analytic Number Theory Research
Spectral Theory in Mathematical Physics
Quantum chaos and dynamical systems
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 30 January 2026