Sums-of-Squares Formulas over Algebraically Closed Fields
Algebraic Geometry
2016-11-01 v2
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.
Keywords
Cite
@article{arxiv.1510.05369,
title = {Sums-of-Squares Formulas over Algebraically Closed Fields},
author = {Melissa Lynn},
journal= {arXiv preprint arXiv:1510.05369},
year = {2016}
}