Pfister's theorem fails in the Hermitian case
Complex Variables
2012-01-31 v2 Algebraic Geometry
Abstract
We show that the Hermitian analogue of a famous result of Pfister fails. To do so we provide a Hermitian symmetric polynomial of total degree 2d such that any non-zero multiple of it cannot be written as a Hermitian sum of squares with fewer than squares.
Cite
@article{arxiv.1010.3215,
title = {Pfister's theorem fails in the Hermitian case},
author = {John P. D'Angelo and Jiri Lebl},
journal= {arXiv preprint arXiv:1010.3215},
year = {2012}
}
Comments
7 pages, to appear in Proc. Amer. Math. Soc., improved exposition in the proof