Riemann Zeros, Quantum Chaos, Functional Determinants & Trace Formula

Abstract

In this paper, I study the relation between the Guzwiller Trace for a dynamical system and the Riemann-Weil trace formula for the Riemann zeros. Using the Bohr-Sommerfeld quantization condition, the WKB rules and fractional calculus, I obtain a method to define implicitly a potential f ^-1(x) for a Hamiltonian in one dimension. I then apply this method to define a Hamiltonian whose energies are the square of the Riemann zeros (imaginary part) E_n=γ_n². I further show that for big ‘x’ the potential is very close to an exponential function.