Nontrivial zeros of the Riemann zeta function on the celestial circle

Abstract

In this short letter, we reformulate the Riemann zeta function using the holographic framework of the celestial conformal field theory. For spacetime dimension larger than our Minkowski spacetime $M^4$, the Riemann zeta function is connected with the sum of the conformal primary wavefunctions evaluated over a chain of points on the holographic boundary. Using analytic continuation, it follows that the nontrivial zeros of the Riemann zeta function is connected with the scaling dimension of conformal operators on the celestial circle. We discuss possible considerations with the spectrum of the celestial conformal field theory, number theory and topology.