  Using the technology of harmonic analysis, we derive a crossing equation that
acts only on the scalar primary operators of any two-dimensional conformal
field theory with $U(1)^c$ symmetry. From this crossing equation, we derive
bounds on the scalar gap of all such theories. Rather remarkably, our crossing
equation contains information about all nontrivial zeros of the Riemann zeta
function. As a result, we rephrase the Riemann hypothesis purely as a statement
about the asymptotic density of scalar operators in certain two-dimensional
conformal field theories. We discuss generalizations to theories with only
Virasoro symmetry.
