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 $0< {\rm Re}\, s < 1$ (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.