@**techreport**{RISC5884,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}

}