MONOMIALS AS SUMS OF k-POWERS OF FORMS
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چکیده
Motivated by recent results on the Waring problem for polynomial rings [FOS12] and representation of monomial as sum of powers of linear forms [CCG12], 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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تاریخ انتشار 2015