The matrix analogs of Weierstrass's zeta and sigma functions are introduced. It is proved that in the case of
Z
n×Z
n-symmetry the classical
-matrix coincides with the matrix zeta-function, whereas the quantum
R-matrix is expressible as a ratio of matrix sigma-functions. The obtained formulas are considered to be the result of averaging over the period lattice.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 133, pp. 258–276, 1984.