Phenomenological formula for quantum Hall resistivity based on the Riemann zeta function

Abstract

We propose a formula constructed out of elementary functions that captures many of the detailed features of the transverse resistivity ρ xy for the integer quantum Hall effect. It is merely a phenomenological formula in the sense that it is not based on any transport calculation for a specific class of physical models involving electrons in a disordered landscape, thus, whether a physical model exists which realizes this resistivity remains an open question. Nevertheless, since the formula involves the Riemann zeta function and its non-trivial zeros play a central role, it is amusing to consider the implications of the Riemann hypothesis in light of it.