A novel integral representation suitable for the study of asymptotic ($L/L_{0}\,{\gg}\,1$, $L$ being the plasma length and $L_{0}$ the basic gain length) stability of the inhomogeneous three-wave interaction is formulated and applied to the special case of uniform gain and ramp wavenumber mismatch. The absolute instability condition is $\kappa L_{0} \,{<}\, \pi /8$ ($\kappa$ being the mismatch gradient), with the wave conversion performed in a zone of width $4/\kappa L_{0}$ located at the boundary of wave incidence.