Pfister's theorem fails in the Hermitian case

John P. D'angelo, Jiří Lebl

Research output: Contribution to journalArticlepeer-review


We show that the Hermitian analogue of a famous result of Pfister fails. To do so we provide a Hermitian symmetric polynomial r of total degree 2d such that any nonzero multiple of it cannot be written as a Hermitian sum of squares with fewer than d + 1 squares.

Original languageEnglish (US)
Pages (from-to)1151-1157
Number of pages7
JournalProceedings of the American Mathematical Society
Issue number4
StatePublished - Apr 2012


  • Hermitian forms
  • Hermitian length
  • Hilbert's 17-th problem
  • Huang lemma
  • Sums of squares

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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