Finiteness of Hilbert functions for generalized Cohen-Macaulay modules

We give effective bounds on the higher Hilbert coefficients of finitely generated modules over Noetherian local rings (A, m) with respect to m-primary ideals, in terms of the multiplicity, dimension and the lengths of local cohomology modules. We similarly bound the Castelnuovo-Mumford regularity of the associated Rees modules.