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arXiv · 1510.05369

Sums-of-Squares Formulas over Algebraically Closed Fields

Melissa Lynn
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Abstract

In this paper, we consider whether existence of a sums-of-squares formula depends on the base field. We reformulate the question of existence as a question in algebraic geometry. We show that, for large enough p, existence of sums-of-squares formulas over algebraically closed fields is independent of the characteristic. We make the bound on p explicit, and we prove that the existence of a sums-of-squares formula of fixed type over an algebraically closed field is theoretically (though not practically) computable.

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Melissa Lynn. 2016-10-31. Sums-of-Squares Formulas over Algebraically Closed Fields. https://arxiv.org/abs/1510.05369

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