## Pfister’s theorem fails in the Hermitian case

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- by John P. D’Angelo and Jiří Lebl PDF
- Proc. Amer. Math. Soc.
**140**(2012), 1151-1157 Request permission

## Abstract:

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.## References

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## Additional Information

**John P. D’Angelo**- Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 61801
- MR Author ID: 53760
- Email: jpda@math.uiuc.edu
**Jiří Lebl**- Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 61801
- Address at time of publication: Department of Mathematics, University of California, San Diego, 9500 Gilman Drive #0112, La Jolla, California 92093-0112
- MR Author ID: 813143
- ORCID: 0000-0002-9320-0823
- Email: jlebl@math.uiuc.edu, jlebl@math.ucsd.edu
- Received by editor(s): July 6, 2010
- Received by editor(s) in revised form: October 8, 2010, and December 22, 2010
- Published electronically: April 1, 2011
- Communicated by: Franc Forstneric
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**140**(2012), 1151-1157 - MSC (2010): Primary 12D15, 14P05, 15B57, 32V15
- DOI: https://doi.org/10.1090/S0002-9939-2011-10841-4
- MathSciNet review: 2869101