SUMS OF SQUARES OVER TOTALLY REAL FIELDS ARE RATIONAL SUMS OF SQUARES
by
Christopher J. Hillar
BibTeX
@MISC{Hillar_sumsof,
author = {Christopher J. Hillar},
title = {SUMS OF SQUARES OVER TOTALLY REAL FIELDS ARE RATIONAL SUMS OF SQUARES},
year = {}
}
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Abstract
Abstract. Let K be a totally real number field with Galois closure L. We prove that if f ∈ Q[x1,..., xn] is a sum of m squares in K[x1,..., xn], then f is a sum of 4m · 2 [L:Q]+1([L: Q] + 1 2 squares in Q[x1,..., xn]. Moreover, our argument is constructive and generalizes to the case of commutative K-algebras. This result gives a partial resolution to a question of Sturmfels on the algebraic degree of certain semidefinite programing problems. 1.
