Abstract
The starting point of this article is an unpublished result of G. Halász stating that if Ω ⊂ C is a fixed lattice, there are n ≥ 3 given points (s i , 1 ≤ i ≤ n) different modulo Ω and there are given values w i ∈ C, then there is a function f elliptic with respect to Ω 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 ≠ j, 1 ≤ i ≤ n, but w j ≠ w with some w ∈ 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.
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Acknowledgements
I would like to thank Professor G. Halász for showing and allowing me to use his unpublished result and its proof. Research was partially supported by the Hungarian National Foundation for Scientific Research (OTKA) Grants No. T032236, T042750, T043623, K72731 and T049693.