Hilbert Coefficients and Depths of Form Rings.

We present short and elementary proofs of two theorems of Huckaba and Marley, while generalizing them at the same time to the case of a module. The theorems concern a characterization of the depth of the associated graded ring of a Cohen-Macaulay module, with respect to a Hilbert filtration, in terms of the Hilbert coefficient e₁. As an application, we derive bounds on the higher Hilbert coefficient e_i in terms of e₀. [ABSTRACT FROM AUTHOR]