  Populations of phase oscillators interacting globally through a general
coupling function $f(x)$ have been considered. In the absence of precessing
frequencies and for odd-coupling functions there exists a Lyapunov functional
and the probability density evolves toward stable stationary states described
by an equilibrium measure. We have then proposed a family of exactly solvable
models with singular couplings which synchronize more easily as the coupling
becomes less singular. The stationary solutions of the least singular coupling
considered, $f(x)=$ sign$(x)$, have been found analytically in terms of
elliptic functions. This last case is one of the few non trivial models for
synchronization dynamics which can be analytically solved.
