Archivio Istituzionale della RicercaMotivated 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 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.
Monomials as sum of k-th powers of forms / Carlini, Enrico; Oneto, A.. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - STAMPA. - 43:2(2015), pp. 650-658. [10.1080/00927872.2013.842247]
Monomials as sum of k-th powers of forms
CARLINI, ENRICO;
2015
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 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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https://hdl.handle.net/11583/2580541
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