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}
}