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We study the correlation functions of su(2) invariant spin-s chains in thethermodynamic limit. We derive non-linear integral equations for an auxiliarycorrelation function $\omega$ for any spin s and finite temperature T. For thespin-3/2 chain for arbitrary temperature and zero magnetic field we obtainalgebraic expressions for the reduced density matrix of two-sites. In the zerotemperature limit, the density matrix elements are evaluated analytically andappear to be given in terms of Riemann's zeta function values of even and oddarguments.

Correlation functions of the integrable spin-s chain