English

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 rr of total degree 2d such that any non-zero multiple of it cannot be written as a Hermitian sum of squares with fewer than d+1d+1 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

R2 v1 2026-06-21T16:29:08.105Z