Number Theory pp 325-349 | Cite as
Pfister’s Work on Sums of Squares
Chapter
Abstract
Historically the theory of quadratic forms was regarded as a topic in number theory. However, Witt’s paper “Theorie der quadratischen Formen in beliebigen Körpern” of 1937[15] opened up a new chapter in the theory: that of combining the number theoretic aspect with the algebraic development, by the creation of the famous Witt ring.
Keywords
Division Ring Bilinear Function Normed Algebra Pfister Form Algebraic Development
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References
- [1]J.F. Adams, Vector fields on Sphere, Annals of Maths 75 (1962), 603–632.MATHCrossRefGoogle Scholar
- [2]A.A. Albert (editor), Studies in Modern Algebra, vol. 2, MAA Studies in Maths (1963).Google Scholar
- [3]E. Artin, Uber die Zerlegung definiter Funktionen in Quadrate, Hamb. Abh. 5 (1927), 100–115.CrossRefGoogle Scholar
- [4]J.W.S. Cassels, On the representation of rational functions as sums of squares, Acta Arith. 9 (1964), 79–82.MathSciNetMATHGoogle Scholar
- [5]L.E. Dickson, On quaternions and their generalizations and the history of the 8-square theorem, Annals of Maths. 20 (1919), 155–171.MATHCrossRefGoogle Scholar
- [6]Adolf Hurwitz, Uber der Komposition der Quadratischen Formen von beliebig vielen Variabeln, Nachrichten von der Königlichen Gessellschaft der Wissenschaften in Göttingen (1898), 309–316; = Math. werke, II 565–571.Google Scholar
- [7]A. Pfister, Zur Darstellung von- I also Summe von Quadraten in einem Körper, JLMS, 40 (1965), 159–165.MathSciNetMATHGoogle Scholar
- [8]A. Pfister, Zur Darstellung definiter Funktionen als Summe Von Quadraten, Inventiones Math. 4 (1967), 224–236.MathSciNetCrossRefGoogle Scholar
- [9]A. Pfister, Hilbert’s 17th problem and related problem on definite forms, Proc. of Symposia in Pure Maths. 28 (1976), 483–489.MathSciNetGoogle Scholar
- [10]A. Pfister, Multiplicative quadratische Formen, Arch. Math. 16 (1965), 363–370.MathSciNetMATHCrossRefGoogle Scholar
- [11]A. Pfister, Quadratrische Fromen in beliebigen Körpern, Inventiones Maths. 1 (1966), 116–132.MathSciNetMATHCrossRefGoogle Scholar
- [12]A.R. Rajwade, A note on the Stufe of quadratic fields. Indian J. Pure and App. Maths. 6 (1975), 725–6.MathSciNetMATHGoogle Scholar
- [13]A.R. Rajwade, Squares, London Math Soc. Lecture note series no. 171, (1993).Google Scholar
- [14]J. Radon, Lineare Scharen orthogonaler Matrizen, Abh. Math. Sem Univ. Hamburg 1 (1922), 1–14.CrossRefGoogle Scholar
- [15]E. Witt, Theorie der quadratischen Formen in beliebigen Körpern, J. reine angew. Math. 17 6 (1937), 31–34.Google Scholar
- [16]Paul Yiu, On the product of 2 sums of 16 squares as a sum of squares on integral bilinear forms, Quart. J. Maths. (2) 41 (1990), 463–500.MATHCrossRefGoogle Scholar
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