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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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


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.
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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:
  • 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:,
  • 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:
  • MathSciNet review: 2869101