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

 

A new proof of a theorem of Cassels and Pfister


Author: Larry J. Gerstein
Journal: Proc. Amer. Math. Soc. 41 (1973), 327-328
MSC: Primary 12E05; Secondary 10C05
MathSciNet review: 0319952
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Abstract: This note uses the theory of quadratic forms over Dedekind domains to give a new proof of a theorem of Cassels and Pfister on the representation of polynomials in terms of squares of rational functions.


References [Enhancements On Off] (What's this?)

  • [1] E. Artin, Über die Zerlegung definiter Funktionen in Quadrate, Abh. Math. Sem. Hamburg 5 (1927), 100-115.
  • [2] J. W. S. Cassels, On the representation of rational functions as sums of squares, Acta Arith. 9 (1964), 79–82. MR 0162791 (29 #95)
  • [3] Manfred Knebusch, Grothendieck- und Wittringe von nichtausgearteten symmetrischen Bilinearformen, S.-B. Heidelberger Akad. Wiss. Math.-Natur. Kl. 1969/70 (1969/1970), 93–157 (German). MR 0271118 (42 #6001)
  • [4] Morris Newman, Integral matrices, Academic Press, New York-London, 1972. Pure and Applied Mathematics, Vol. 45. MR 0340283 (49 #5038)
  • [5] O. T. O'Meara, Introduction to quadratic forms, Die Grundlehren der math. Wissenschaften, Band 117, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 27 #2485.
  • [6] Albrecht Pfister, Multiplikative quadratische Formen, Arch. Math. (Basel) 16 (1965), 363–370 (German). MR 0184937 (32 #2408)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0319952-7
PII: S 0002-9939(1973)0319952-7
Article copyright: © Copyright 1973 American Mathematical Society