Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2014, Number 2, Pages 9–14 (Mi vmumm303)  
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Representation of monomials as a sum of powers of linear forms

S. B. Gashkov, E. T. Shavgulidze

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: We prove that the product of $n$ complex variables can be represented as a sum of $m=2^{n-1}$ $n$-powers of linear forms of $n$ variables and for any $m< 2^{n-1}$ there is no such identity with $m$ summands being $n$th powers of linear forms.
Key words: linear forms, monomials, representation as sum of powers, low bounds.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00508
11-01-00792а
Received: 01.10.2012
English version:
Moscow University Mathematics Bulletin, 2014, Volume 69, Issue 2, Pages 51–55
DOI: https://doi.org/10.3103/S0027132214020028
Bibliographic databases:
Document Type: Article
UDC: 519.95
Language: Russian
Citation: S. B. Gashkov, E. T. Shavgulidze, “Representation of monomials as a sum of powers of linear forms”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2014, no. 2, 9–14; Moscow University Mathematics Bulletin, 69:2 (2014), 51–55
Citation in format AMSBIB
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\paper Representation of monomials as a sum of powers of linear forms
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\pages 9--14
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\jour Moscow University Mathematics Bulletin
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\pages 51--55
\crossref{https://doi.org/10.3103/S0027132214020028}
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