One-loop effective action and the Riemann Zeros
  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. 
J. G. Due\~nas, N. F. Svaiter, G. Menezes
math-ph hep-th math.MP