  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.
