In this note we discuss an analog of the classical Waring problem for C[x_0..x_n]. Namely, we show that a general homogeneous polynomial p in C[x_0..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_n]. Noticeably, k^n coincides with the number obtained by naive dimension count.
On the Waring problem for polynomials rings / R. Froberg; G. Ottaviani; B. Shapiro. - In: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA. - ISSN 0027-8424. - STAMPA. - 109:(2012), pp. 5600-5602. [10.1073/pnas.1120984109]
On the Waring problem for polynomials rings
OTTAVIANI, GIORGIO MARIA;
2012
Abstract
In this note we discuss an analog of the classical Waring problem for C[x_0..x_n]. Namely, we show that a general homogeneous polynomial p in C[x_0..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_n]. Noticeably, k^n coincides with the number obtained by naive dimension count.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
sumpowers3.pdf
Accesso chiuso
Tipologia:
Versione finale referata (Postprint, Accepted manuscript)
Licenza:
Tutti i diritti riservati
Dimensione
291.37 kB
Formato
Adobe PDF
|
291.37 kB | Adobe PDF | Richiedi una copia |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
