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Sums of squares of linear forms: the quaternions approach

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Fernando Galván, José Francisco and Ruiz Sancho, Jesús María and Scheiderer, Claus (2006) Sums of squares of linear forms: the quaternions approach. UCM GT preprint . pp. 1-15. (Unpublished)

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Official URL: http://www.mat.ucm.es/~jesusr/pdfs/preprints/IHP.pdf


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Abstract

Let A = k[y] be the polynomial ring in one single variable y over a field k. We discuss the number of squares needed to represent sums of squares of linear forms with coefficients in the ring A. We use quaternions to obtain bounds when the Pythagoras number of A is ≤ 4. This provides bounds for the Pythagoras number of algebraic curves and algebroid surfaces over k.


Item Type:Article
Uncontrolled Keywords:Pythagoras number, Pfister bound, quaternions
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:21528
Deposited On:23 May 2013 15:41
Last Modified:17 Dec 2018 18:57

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