#####
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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