A new proof of a theorem of Cassels and Pfister
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- by Larry J. Gerstein PDF
- Proc. Amer. Math. Soc. 41 (1973), 327-328 Request permission
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
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E. Artin, Über die Zerlegung definiter Funktionen in Quadrate, Abh. Math. Sem. Hamburg 5 (1927), 100-115.
- J. W. S. Cassels, On the representation of rational functions as sums of squares, Acta Arith. 9 (1964), 79–82. MR 162791, DOI 10.4064/aa-9-1-79-82
- 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
- Morris Newman, Integral matrices, Pure and Applied Mathematics, Vol. 45, Academic Press, New York-London, 1972. MR 0340283 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.
- Albrecht Pfister, Multiplikative quadratische Formen, Arch. Math. (Basel) 16 (1965), 363–370 (German). MR 184937, DOI 10.1007/BF01220043
Additional Information
- © Copyright 1973 American Mathematical Society
- 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