Abstract
Artin solved Hilbert’s 17th problem, proving that a real polynomial in variables that is positive semidefinite is a sum of squares of rational functions, and Pfister showed that only squares are needed.
In this paper, we investigate situations where Pfister’s theorem may be improved. We show that a real polynomial of degree in variables that is positive semidefinite is a sum of squares of rational functions if . If is even or equal to or , this result also holds for .
Citation
Olivier Benoist. "On Hilbert's 17th problem in low degree." Algebra Number Theory 11 (4) 929 - 959, 2017. https://doi.org/10.2140/ant.2017.11.929
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