Proceedings of the American Mathematical Society

Author(s): Christopher J. Hillar
Journal: Proc. Amer. Math. Soc. 137 (2009), 921-930.
MSC (2000): Primary 12Y05, 12F10, 11E25, 13B24
Posted: September 25, 2008
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Abstract: Let

be a totally real number field with Galois closure

. We prove that if $f \in \mathbb{Q}[x_1,\ldots,x_n]$ is a sum of

squares in $K[x_1,\ldots,x_n]$ , then

is a sum of

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 12Y05, 12F10, 11E25, 13B24

Christopher J. Hillar
Affiliation: Department of Mathematics, Texas A\&M University, College Station, Texas 77843
Email: chillar@math.tamu.edu

DOI: 10.1090/S0002-9939-08-09641-X
PII: S 0002-9939(08)09641-X
Keywords: Rational sum of squares, semidefinite programming, totally real number field
Received by editor(s): June 11, 2007,
Received by editor(s) in revised form: March 31, 2008
Posted: September 25, 2008
Additional Notes: The author was supported under a National Science Foundation Postdoctoral Research Fellowship.
Communicated by: Bernd Ulrich
Copyright of article: Copyright 2008, American Mathematical Society

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