Supersymmetry and the Riemann zeros on the critical line

Abstract

We propose a new way of studying the Riemann zeros on the critical line using ideas from supersymmetry. Namely, we construct a supersymmetric quantum mechanical model whose energy eigenvalues correspond to the Riemann zeta function in the strip $0<\mathrm{Re}s<1$ (in the complex parameter space) and show that the zeros on the critical line arise naturally from the vanishing ground state energy condition in this model.

arXiv comment5 pages, title modified, version to be published in Physics Letters B

References in corpus (4)

• Hamiltonian for the zeros of the Riemann zeta function
• Riemann Zeta Function
• The Berry-Keating operator on $L^2(\rz_>,\ud x)$ and on compact quantum graphs with general self-adjoint realizations
• Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

Cited by in corpus (5)

• Supersymmetric quantum mechanics and the Riemann hypothesis
• A symmetry perspective of the Riemann zeros
• Hamiltonian for the Hilbert-Pólya Conjecture
• On the nontrivial zeros of the Dirichlet eta function
• Riemann Hypothesis, Modified Morse Potential and Supersymmetric Quantum Mechanics