Monomials as sum of k-th powers of forms

Abstract

Motivated by recent results on the Waring problem for polynomial rings and representation of monomial as sum of powers of linear forms, we consider the problem of presenting monomials of degree kd as sums of k-th powers of forms of degree d. We produce a general bound on the number of summands for any number of variables which we refine in the two variables case. We completely solve the k=3 case for monomials in two and three variables.

8 pages

References in corpus (1)

• On the Waring problem for polynomial rings

Cited by in corpus (2)

• On generic and maximal k-ranks of binary forms
• Algebraic stories from one and from the other pockets