H.E.Boos, V.E.Korepin Evaluation of Integrals Representing Correlations in XXX Heisenberg Spin Chain (86K, LATEX) ABSTRACT. We study XXX Heisenberg spin 1/2 anti-ferromagnet. We evaluate a probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in thermodynamics limit. We prove that for short strings the probability can be expressed in terms of Riemann zeta function with odd arguments.