Séminaire Lotharingien de Combinatoire, B21a (1989), 17 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1990, 413/S-21, p. 14-18.]

Andreas Dress and Johannes Grabmeier

On zero-testing and interpolation of sums of characters

Abstract. Motivated by an amazing result of D. Y. Grigoriev and M. Karpinski, the interpolation problem for k-sparse multivariate polynomials has received some attention in recent years. In this note we want to show that essentially all of the results obtained so far hold more generally for k-sparse sums of characters of abelian monoids, thereby providing a useful unified approach to this active field of research. As it turns out the basic ingredients of this approach are the construction of distinction sets for characters and zero-test sets for k-sparse character sums.

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