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Sums of squares of linear forms.

Fernando Galván, José Francisco and Ruiz Sancho, Jesús María and Scheiderer, Claus (2006) Sums of squares of linear forms. Mathematical Research Letters, 13 (5-6). pp. 947-956. ISSN 1073-2780

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Sums of squares, quadratic forms, level; Pythagoras numbers;local henselian rings.
Subjects:Sciences > Mathematics > Number theory
Sciences > Mathematics > Algebraic geometry
ID Code:15130
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