Geodesic
Sets of Hilbert series and their applications
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 3, pp. 143-156

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We consider graded finitely presented algebras and modules over a field. Under some restrictions, the set of Hilbert series of such algebras (or modules) becomes finite. Claims of that type imply the rationality of Hilbert and Poincaré series of some algebras and modules, including the periodicity of Hilbert functions of many (e.g., Noetherian) modules and algebras of linear growth. 
@article{FPM_2004_10_3_a6,
     author = {D. I. Piontkovskii},
     title = {Sets of {Hilbert} series and their applications},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {143--156},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2004_10_3_a6/}
}
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D. I. Piontkovskii. Sets of Hilbert series and their applications. Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 3, pp. 143-156. http://geodesic.mathdoc.fr/item/FPM_2004_10_3_a6/