A Hilbert–Polya Operator derived from a Prime Oscillator System
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.
Authors
- Guillermo Garcia
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-03-13
- DOI
- https://doi.org/10.5281/zenodo.18996678
- Primary Topic
- Spectral Theory in Mathematical Physics
- Type
- article
- Field-Weighted Citation Impact
- 0.00