Hilbert series of modules over positively graded polynomials rings

Abstract

In this note, we give examples of formal power series satisfying certain conditions that cannot be realized as Hilbert series of finitely generated modules. This answers to the negative a question raised in a recent article by the second and the third author. On the other hand, we show that the answer is positive after multiplication with a scalar.Comment: Minor corrections. To appear in J. Algebr