Interpolation by elliptic functions

The starting point of this article is an unpublished result of G. Halasz stating that if Omega subset of C is a fixed lattice, there are n >= 3 given points (s(i), 1 <= i <= n) different modulo Omega and there are given values w(i) is an element of C, then there is a function f elliptic with respect to Omega of order at most n - 1 such that f(s(i)) = w(i) for 1 <= i <= n. We prove that if n >= 6, then under the obvious necessary condition there is no 1 <= j <= n such that w(i) = w for every i not equal j, 1 <= i <= n, but w(j) not equal w with some w is an element of C, one can improve the upper bound n - 1 for the order of f, i.e. one can give an interpolating f of order at most n - 2.