Tight bounds for rational sums of squares over totally real fields

Ronan Quarez (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

Let 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.

Mots clés: totally real number field.; Rational sum of squares; semidefinite programming; totally real number field

Domaines: Autre [cs.OH]; Anneaux et algèbres [math.RA]

Ronan Quarez. Tight bounds for rational sums of squares over totally real fields: Tight bounds for rational sums of squares over totally real fields. Rendiconti del Circolo Matematico di Palermo, 2010, 59 (3), pp.377-388. ⟨hal-00403920⟩