  The Hellings and Downs correlation curve describes the correlation of the
timing residuals from pairs of pulsars as a function of their angular
separation on the sky and is a smoking-gun signature for the detection of an
isotropic stochastic background of gravitational waves. We show that it can be
easily obtained from realizing that Lorentz transformations are conformal
transformations on the celestial sphere and from the conformal properties of
the two-point correlation of the timing residuals. This result allows several
generalizations, e.g. the calculation of the three-point correlator of the time
residuals and the inclusion of additional polarization modes (vector and/or
scalar) arising in alternative theories of gravity.
