Hilbert–Pólya conjecture relating zeta zeros to a Hermitian operator

Establish the Hilbert–Pólya conjecture by rigorously demonstrating a connection between the distribution of nontrivial zeros of the Riemann zeta function and the eigenvalues of a specific Hermitian operator.

Background

The authors motivate their construction of a Hermitian “chaotic operator” by invoking the Hilbert–Pólya conjecture, which suggests a spectral interpretation of the nontrivial zeros of the Riemann zeta function. They argue that properties of their operator (Hermiticity, diagonalizability) align with this conjectural framework.

This conjecture is presented as a guiding open question that, if resolved, could lead to a proof of the Riemann Hypothesis via spectral or operator-theoretic methods.