Bounding the rational sums of squares over totally real fields

Details Bounding the rational sums of squares over totally real fields Bounding the rational sums of squares over totally real fields

2009-07-14

arxiv.org/abs/0907.2336v1

Mathematics

Number Theory

Scientific paper

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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