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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Laws of inertia in higher degree binary forms


Author: Bruce Reznick
Journal: Proc. Amer. Math. Soc. 138 (2010), 815-826
MSC (2010): Primary 11E76, 15A21
Published electronically: November 3, 2009
MathSciNet review: 2566547
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Abstract: We consider representations of real forms of even degree as a linear combination of powers of real linear forms, counting the number of positive and negative coefficients. We show that the natural generalization of Sylvester's Law of Inertia holds for binary quartics but fails for binary sextics.


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Additional Information

Bruce Reznick
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Email: reznick@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10186-7
PII: S 0002-9939(09)10186-7
Received by editor(s): June 30, 2009
Published electronically: November 3, 2009
Communicated by: Ken Ono
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.