Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 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

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
11-01-00792


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English version:
Moscow University Mathematics Bulletin, 2014, 69:2, 51–55

Bibliographic databases:

UDC: 519.95
Received: 01.10.2012

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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\by S.~B.~Gashkov, E.~T.~Shavgulidze
\paper Representation of monomials as a sum of powers of linear forms
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2014
\issue 2
\pages 9--14
\mathnet{http://mi.mathnet.ru/vmumm303}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3299483}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2014
\vol 69
\issue 2
\pages 51--55
\crossref{https://doi.org/10.3103/S0027132214020028}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899864049}


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    This publication is cited in the following articles:
    1. A. V. Seliverstov, “Kubicheskie formy bez monomov ot dvukh peremennykh”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:1 (2015), 71–77  mathnet  elib
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