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- W3100792570 abstract "Artin solved Hilbert's 17th problem, proving that a real polynomial in $n$ variables that is positive semidefinite is a sum of squares of rational functions, and Pfister showed that only $2^n$ squares are needed. In this paper, we investigate situations where Pfister's theorem may be improved. We show that a real polynomial of degree $d$ in $n$ variables that is positive semidefinite is a sum of $2^n-1$ squares of rational functions if $dleq 2n-2$. If $n$ is even, or equal to $3$ or $5$, this result also holds for $d=2n$." @default.
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- W3100792570 date "2017-06-18" @default.
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- W3100792570 title "On Hilbert’s 17th problem in low degree" @default.
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- W3100792570 doi "https://doi.org/10.2140/ant.2017.11.929" @default.
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