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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
DOI: https://doi.org/10.1090/S0002-9939-1973-0319952-7
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 29 #95. MR 0162791 (29:95)
  • [3] M. Knebusch, Grothendieck- und Wittringe von nichtausgearteten symmetrischen Bilinearformen, S.-B. Heidelberger Akad. Wiss. Math.-Natur. Kl. 1969/70, 93-157. MR 42 #6001. MR 0271118 (42:6001)
  • [4] M. Newman, Integral matrices, Academic Press, New York, 1972. 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] A. Pfister, Multiplikative quadratische Formen, Arch. Math. 16 (1965), 363-370. MR 32 #2408. MR 0184937 (32:2408)

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DOI: https://doi.org/10.1090/S0002-9939-1973-0319952-7
Article copyright: © Copyright 1973 American Mathematical Society

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