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On the Waring problem for polynomial rings
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
2012 (English)In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 109, no 15, 5600-5602 p.Article in journal (Refereed) Published
Abstract [en]

In this note we discuss an analog of the classical Waring problem for C[x(0),x(1),..., x(n)]- Namely, we show that a general homogeneous polynomial p is an element of C[x(0),x(1),..,x(n)] of degree divisible by k >= 2 can be represented as a sum of at most k(n) k-th powers of homogeneous polynomials in C[x(0),x(1),...,x(n)]. Noticeably, k(n) coincides with the number obtained by naive dimension count.

Place, publisher, year, edition, pages
2012. Vol. 109, no 15, 5600-5602 p.
Keyword [en]
sum of powers, sum of squares, Veronese embedding
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-76051DOI: 10.1073/pnas.1120984109ISI: 000302533500017OAI: oai:DiVA.org:su-76051DiVA: diva2:525784
Note
3Available from: 2012-05-09 Created: 2012-05-08 Last updated: 2017-12-07Bibliographically approved

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