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arXiv · 0907.2336

Bounding the rational sums of squares over totally real fields

Ronan Quarez
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Abstract

Let K be a totally real Galois number field. C. J. Hillar proved that if f in Q[x_1,...,x_n] is a sum of m squares in K[x_1,...,x_n], then f is a sum of N(m) squares in Q[x_1,...,x_n]. Modifying Hillar's proof, we improve the improve the bound given for N(m), the proof being constructive as well.

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Ronan Quarez. 2009-07-14. Bounding the rational sums of squares over totally real fields. https://arxiv.org/abs/0907.2336

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