author = {J. Capco and C. Scheiderer},
title = {{Sum of Squares over Rationals}},
language = {english},
abstract = {Recently it has been shown that a multivariate (homogeneous) polynomial with rational coefficients that can be written as a sum of squares of forms with real coefficients, is not necessarily a sum of squares of forms with rational coefficients. Essentially, only one construction for such forms is known, namely taking the $K/\Q$-norm of a sufficiently general form with coefficients in a number field $K$. Whether this construction yields a form with the desired properties depends on Galois-theoretic properties of $K$ that are not yet well understood. We construct new families of examples, and we shed new light on some well-known open questions. },
year = {2019},
institution = {RISC},
length = {0},
url = {https://www3.risc.jku.at/~jcapco/public_files/ss18/sosq.html}