One-loop effective action and the Riemann Zeros

Abstract

We present a remarkable connection between the asymptotic behavior of the Riemann zeros and one-loop effective action in Euclidean scalar field theory. We show that in a two-dimensional space, the asymptotic behavior of the Fourier transform of two-point correlation functions fits the asymptotic distribution of the non-trivial zeros of the Riemann zeta function. We work out an explicit example, namely the non-linear sigma model in the leading order in $1/N$ expansion.

References in corpus (2)

• The H=xp model revisited and the Riemann zeros
• H = x p with interaction and the Riemann zeros

Cited by in corpus (1)

• Functional equations for regularized zeta-functions and diffusion processes