%0 Journal Article
%A Fernando Galván, José Francisco
%A Ruiz Sancho, Jesús María
%A Scheiderer, Claus
%T Sums of squares of linear forms
%D 2006
%@ 1073-2780
%U https://hdl.handle.net/20.500.14352/49900
%X Let k be a real field. We show that every non-negative homogeneous quadratic polynomial f (x(1),..., x(n)) with coefficients in the polynomial ring k[t] is a sum of 2n center dot tau(k) squares of linear forms, where tau(k) is the supremum of the levels of the finite non-real field extensions of k. From this result we deduce bounds for the Pythagoras numbers of affine curves over fields, and of excellent two-dimensional local henselian rings.
%~