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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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Official URL: http://mrlonline.org/mrl/2006-013-006/2006-013-006-009.pdf

## 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 |
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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 |

Deposited On: | 08 May 2012 10:33 |

Last Modified: | 22 Mar 2019 18:51 |

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