On the coefficients of the Hilbert polynomial Original Research Article

Let (A, m) be Cohen-Macaulay local ring with maximal ideal m and dimension d. It is well known that for n> 0, the length of the A-module A/mn is given by image. The integers paper an ei are called the Hilbert coefficients of A. In this paper an upper bound is given for e2 in terms of e0, e1 and the embedded codimension h of A. If d ≤ 2 and the bound is reached, A has a specified Hilbert function. Similarly, in the one-dimensional case, we study the extremal behaviour with respect to the known inequality image.