Abstract
Motivated by recent results on the Waring problem for polynomial rings [Citation4] and representation of monomial as sum of powers of linear forms [Citation3], we consider the problem of presenting monomials of degree kd as sums of kth-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.
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ACKNOWLEDGMENTS
The authors wish to thank Froeberg and Shapiro for their many helpful suggestions and wonderful ideas.
Notes
Communicated by R. Piene.