Solutions of the triangle equations with $\mathbb Z_n\times\mathbb Z_n$-symmetry as the matrix analogues of the Weierstrass zets and sigma functions

The matrix analogues of the Weierstrass zeta and sigma functions are introduced and studied. It is proved in the case of $\mathbb Z_n\times\mathbb Z_n$ symmetry that the classical $r$-matrix coincides with the matrix zeta function and that the quantum $R$-matrix can be represented as the ratio of matrix sigma functions. The obtained formulae are interpreted as the result of averaging over the lattice in $\mathbb C$.