In case of the ring of polynomials with complex coefficients an analog of the classical number-theoretical Waring problem asks the following. Given the positive integers $k, d, n$, find/estimate how many homogeneous polynomials of degree $d$ in $n$ variables are needed to be able to present any/almost any homogeneous polynomial of degree $kd$ in $n$ variables as the sum of their $k$-th powers.
