Motivated by recent results on the Waring problem for polynomial rings [4] and representation of monomial as sum of powers of linear forms [3], 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 Sums of k th-Powers of Forms / Carlini, E.; Oneto, A.. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - 2015, 43:2(2015), pp. 650-658. [10.1080/00927872.2013.842247]
Monomials as Sums of k th-Powers of Forms
Oneto A.
2015-01-01
Abstract
Motivated by recent results on the Waring problem for polynomial rings [4] and representation of monomial as sum of powers of linear forms [3], 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.| File | Dimensione | Formato | |
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