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Representation of monomials as a sum of powers of linear forms

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Abstract

It is proved that the product of n complex variables can be represented as a sum of m = 2n−1 n-powers of linear forms of n variables and for any m < 2n−1 there is no such identity with m summands being nth powers of linear forms.

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Author information

Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    S. B. Gashkov & E. T. Shavgulidze

Authors
  1. S. B. Gashkov
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  2. E. T. Shavgulidze
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Corresponding author

Correspondence to S. B. Gashkov.

Additional information

Original Russian Text © S.B. Gashkov, E.T. Shavgulidze, 2014, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2014, Vol. 69, No. 2, pp. 9–14.

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Gashkov, S.B., Shavgulidze, E.T. Representation of monomials as a sum of powers of linear forms. Moscow Univ. Math. Bull. 69, 51–55 (2014). https://doi.org/10.3103/S0027132214020028

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  • DOI: https://doi.org/10.3103/S0027132214020028

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