ИСТИНА

The Poincaré series of a multi-index filtration was first defined in a paper by A.Campillo, F.Delgado and K.Kiyek. Now this definition looks very natural, however, I cannot say that this was so from the very beginning. I'll discuss possible alternative definitions of the Poincaré series (applied when the initial one does not work), some methods to compute them and their relations with topological invariants (say, with monodromy zeta functions). A.Campillo participated in a big part of this history.