Sums of squares over totally real fields are rational sums of squares

Christopher J. Hillar

Let $K$ be a totally real number field with Galois closure $L$. We prove that if $f\in \mathbb{Q}[x_1,...,x_n]$ is a sum of $m$ squares in $K[x_1,...,x_n]$, then $f$ is a sum of \[…