Bounding the rational sums of squares over totally real fields
Abstract
Let K be a totally real Galois number field. C. J. Hillar proved that if f in Q[x1,...,xn] is a sum of m squares in K[x1,...,xn], then f is a sum of N(m) squares in Q[x1,...,xn]. Modifying Hillar's proof, we improve the improve the bound given for N(m), the proof being constructive as well.
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