Reality of the Eigenvalues of the Hilbert-Pólya Hamiltonian

• URL: http://arxiv.org/abs/2408.15135v4
• Date: Mon, 21 Oct 2024 15:46:34 GMT
• Title: Reality of the Eigenvalues of the Hilbert-Pólya Hamiltonian
• Authors: Enderalp Yakaboylu,
• Abstract summary: We propose a Hamiltonian for the Hilbert-P'olya Conjecture. We show that the eigenfunctions of the transformed operator are square-integrable, and crucially, that the eigenvalues are real.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Building on the recent work in~[J. Phys. A: Math. Theor. 57, 235204 (2024)], we propose a Hamiltonian for the Hilbert-P\'olya Conjecture. We demonstrate the existence of a well-defined similarity transformation that renders this Hamiltonian self-adjoint for the nontrivial Riemann zeros. Specifically, we show that the eigenfunctions of the transformed operator are orthogonal and square-integrable, and crucially, that the eigenvalues are real. This represents a significant step toward proving the Riemann Hypothesis.

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