On the Pythagoras number for polynomials of degree 4 in 5 variables

On the Pythagoras number for polynomials of degree 4 in 5 variables

We give an example of a polynomial of degree 4 in 5 variables that is the sum of squares of 8 polynomials and cannot be decomposed as the sum of 7 squares. This improves the current existing lower bound of 7 polynomials for the Pythagoras number \(p(5,4)\).

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Veröffentlicht in:arXiv.org 2023-06
1. Verfasser: Laplagne, Santiago
Format: Artikel
Sprache:eng
Schlagworte:
Lower bounds
Polynomials
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Zusammenfassung:We give an example of a polynomial of degree 4 in 5 variables that is the sum of squares of 8 polynomials and cannot be decomposed as the sum of 7 squares. This improves the current existing lower bound of 7 polynomials for the Pythagoras number \(p(5,4)\).
ISSN:2331-8422