An upper bound for the Waring rank of a form

In this paper we introduce the open Waring rank of a form of degree d in n variables and prove that this rank is bounded from above by n + d - 2 d - 1 - n + d - 6 d - 3 whenever n , d  ≥ 3. This proves the same upper bound for the classical Waring rank of a form, improving the result of Białynicki-B...

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Bibliographic Details
Published in:Archiv der Mathematik 2014-04, Vol.102 (4), p.329-336
Main Author: Jelisiejew, Joachim
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:In this paper we introduce the open Waring rank of a form of degree d in n variables and prove that this rank is bounded from above by n + d - 2 d - 1 - n + d - 6 d - 3 whenever n , d  ≥ 3. This proves the same upper bound for the classical Waring rank of a form, improving the result of Białynicki-Birula and Schinzel (see[ 4 ]) and giving, as far as we know, the best upper bound known.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-014-0632-6