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Proceedings of the American Mathematical Society

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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

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.
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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