The functional equation gives a systematic way to decrease
the power of a polynomial via the ring of differential operators.
This tool has been used to study singularities, multiplier ideals,
local cohomology and zeta functions. In this talk we will discuss a
functional equation for meromorphic equations and several consequences
of its existence. This is joint work with Josep Àlvarez Montaner,
Manuel González Villa, and Edwin León-Cardenal.