A Hilbert–Polya Operator derived from a Prime Oscillator System
Abstract
We construct an explicit self-adjoint operator L= A+ V on ℓ2(N,1/n) arising from a dynamical system of prime oscillators. The free Hamiltonian A= log n generates dilations; the interaction V = Re(TΛ) encodes prime-power firing events via Dirichlet convolution with the von Mangoldt function.
Fields of Study & Subjects
Analytic Number Theory Research
Spectral Theory in Mathematical Physics
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 13 March 2026
- Language
- EN