English

Bounding the rational sums of squares over totally real fields

Number Theory 2009-07-15 v1 Rings and Algebras

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.

Keywords

Cite

@article{arxiv.0907.2336,
  title  = {Bounding the rational sums of squares over totally real fields},
  author = {Ronan Quarez},
  journal= {arXiv preprint arXiv:0907.2336},
  year   = {2009}
}