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Let R be a local, Gorenstein ring with algebraically closed residue field k of characteristic 0 and let P  R (z):= Σ p=0∞ dim k (Tor p  R (k, k))z  p  be its Poincaré series. We compute P  R  when R belongs to a particular class defined in the Introduction, proving its rationality. As a by-product we prove the rationality of P  R  for all local, Gorenstein rings of multiplicity at most 10.

The Poincaré series of a local Gorenstein ring of multiplicity up to 10 is rational