José F. Fernando

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Let k be a real field. We show that every non-negative homogeneous quadratic polynomial f (x 1 ,. .. , xn) with coefficients in the polynomial ring k[t] is a sum of 2n · τ (k) squares of linear forms, where τ (k) is the supre-mum of the levels of the finite non-real field extensions of k. From this result we deduce bounds for the Pythagoras numbers of(More)
We consider the 17th Hilbert Problem for global analytic functions in a modified form that involves infinite sums of squares. Then we prove a local-global principle for an analytic function to be a sum of squares. We deduce that an affirmative solution to the 17th Hilbert Problem for global analytic functions implies the finiteness of the Pythagoras number(More)