  Synchronization of coupled oscillators on a $d$-dimensional lattice with the
power-law coupling $G(r) = g_0/r^\alpha$ and randomly distributed intrinsic
frequency is analyzed. A systematic perturbation theory is developed to
calculate the order parameter profile and correlation functions in powers of
$\epsilon = \alpha/d-1$. For $\alpha \le d$, the system exhibits a sharp
synchronization transition as described by the conventional mean-field theory.
For $\alpha > d$, the transition is smeared by the quenched disorder, and the
macroscopic order parameter $\Av\psi$ decays slowly with $g_0$ as $|\Av\psi|
\propto g_0^2$.
