  This paper is continuation of our previous papers hep-th/0209246 and
hep-th/0304077 .
  We discuss in more detail a new form of solution to the quantum
Knizhnik-Zamolodchikov equation [qKZ] on level -4 obtained in the paper
hep-th/0304077 for the Heisenberg XXX spin chain. The main advantage of this
form is it's explicit reducibility to one-dimensional integrals. We argue that
the deep mathematical reason for this is some special cohomologies of deformed
Jacobi varieties. We apply this new form of solution to the correlation
functions using the Jimbo-Miwa conjecture. A formula (46) for the correlation
functions obtained in this way is in a good agreement with the ansatz for the
emptiness formation probability from the paper hep-th/0209246. Our previous
conjecture on a structure of correlation functions of the XXX model in the
homogeneous limit through the Riemann zeta functions at odd arguments is a
corollary of the formula (46).
