Geodesic
The Poincaré Series Of Stretched Cohen-Macaulay Rings
Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1261-1265

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There are relatively few classes of local rings (R, m) for which the question of the rationality of the Poincaré series where k = R/m, has been settled. (For an example of a local ring with non-rational Poincaré series see the recent paper by D. Anick, “Construction of loop spaces and local rings whose Poincaré—Betti series are nonrational”, C. R. Acad. Sc. Paris 290 (1980), 729-732.) In this note, we compute the Poincaré series of a certain family of local Cohen-Macaulay rings and obtain, as a corollary, the rationality of the Poincaré series of d-dimensional local Gorenstein rings (R, m) of embedding dimension at least e + d – 3, where e is the multiplicity of R. It follows that local Gorenstein rings of multiplicity at most five have rational Poincaré series. 
Sally, Judith D. The Poincaré Series Of Stretched Cohen-Macaulay Rings. Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1261-1265. doi: 10.4153/CJM-1980-094-0
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