Fernando Galván, José FranciscoRuiz Sancho, Jesús MaríaScheiderer, Claus2023-06-202023-06-2020061073-2780https://hdl.handle.net/20.500.14352/49900Let 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.spajournal articlehttp://mrlonline.org/mrl/2006-013-006/2006-013-006-009.pdfhttp://www.intlpress.com/open access511512.7Sums of squaresquadratic formslevelPythagoras numberslocal henselian rings.Teoría de númerosGeometria algebraica1205 Teoría de Números1201.01 Geometría Algebraica