title: On the Waring problem for polynomial rings.
abstract: In this note we discuss an analog of the classical Waring problem for C[x0,x1,...,x(n)]. Namely, we show that a general homogeneous polynomial p ∈ C[x0,x1,...,x(n)] of degree divisible by k≥2 can be represented as a sum of at most k(n) k-th powers of homogeneous polynomials in C[x0,x1,...,x(n)]. Noticeably, k(n) coincides with the number obtained by naive dimension count.
authors.affiliation: Department of Mathematics, Stockholm University, SE-106 91, Stockholm, Sweden.
authors.forename: Ralf
authors.initials: R
authors.lastname: Fröberg
authors.forename: Giorgio
authors.initials: G
authors.lastname: Ottaviani
authors.forename: Boris
authors.initials: B
authors.lastname: Shapiro