Tight bounds for rational sums of squares over totally real fields: Tight bounds for rational sums of squares over totally real fields

International audienceLet K be a totally real Galois number field. C. J. Hillar proved that if f in Q[x_1,\ldots,x_n] is a sum of m squares in K[x_1,\ldots,x_n], then f is a sum of N(m) squares in Q[x_1,\ldots,x_n]. Modifying Hillar's proof, we improve the improve the bound given for N(m), the proof being constructive as well