Jost function, prime numbers and Riemann zeta function

Abstract

The large complex zeros of the Jost function (poles of the S matrix) in the complex wave number-plane for s-wave scattering by truncated potentials are associated to the distribution of large prime numbers as well as to the asymptotic behavior of the imaginary parts of the zeros of the Riemann zeta function on the critical line. A variant of the Hilbert and Polya conjecture is proposed and considerations about the Dirac sea as ``virtual resonances'' are briefly discussed.