We present analytical calculations and numerical simulations for the synchronization of oscillators interacting via a long-range power law interaction on a one-dimensional lattice. We have identified the critical value of the power law exponent αc across which a transition from a synchronized to an unsynchronized state takes place for a sufficiently strong but finite coupling strength in the large system limit. We find αc =3/2. Frequency entrainment and phase ordering are discussed as a function of α1. The calculations are performed using an expansion about the aligned phase state (spin-wave approximation) and a coarse graining approach. We also generalize the spin-wave results to the d -dimensional problem. © 2010 The American Physical Society.