Reality of the Eigenvalues of the Hilbert-Pólya Hamiltonian

Building on the recent work in~[J. Phys. A: Math. Theor. 57, 235204 (2024)], we propose a Hamiltonian for the Hilbert-Pólya Conjecture. We establish the existence of a well-defined similarity transformation that renders this Hamiltonian self-adjoint for the nontrivial Riemann zeros. In particular, w...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-12
Main Author: Yakaboylu, Enderalp
Format: Article
Language:English
Subjects:
Eigenvalues
Eigenvectors
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Building on the recent work in~[J. Phys. A: Math. Theor. 57, 235204 (2024)], we propose a Hamiltonian for the Hilbert-Pólya Conjecture. We establish the existence of a well-defined similarity transformation that renders this Hamiltonian self-adjoint for the nontrivial Riemann zeros. In particular, we explicitly demonstrate that the eigenfunctions of the transformed Hamiltonian are orthogonal and square-integrable, and crucially, that the eigenvalues are real. This represents a significant step toward proving the Riemann Hypothesis.
ISSN:2331-8422