Squares [E-Book] / A.R. Rajwade.
Rajwade, A. R., (author)
Cambridge : Cambridge University Press, 1993
1 online resource (xii, 286 pages)
London Mathematical Society lecture note series ; 171
Full Text
Table of Contents:
  • The theorem of Hurwitz (1898) on the 2, 4, 8-identities
  • The 2n-identities and the Stufe of fields : theorems of Pfister and Cassels
  • Examples of the Stufe of fields and related topics
  • Hilbert's 17th problem and the function fields R(X), Q(X), and R(X, Y)
  • Positive semi-definite functions and sums of squares in R(X1,X2, ..., Xn)
  • Introduction to Hilbert's theorem (1888) in the ring R[X1,X2, ..., Xn]
  • The two proofs of Hilbert's main theorem; Hilbert's own and the other of Choi and Lam
  • Theorems of Reznick and of Choi, Lam and Reznick
  • Theorems of Choi, Calderon and of Robinson
  • The Radon function and the theorem of Hurwitz-Radon (1922-23)
  • Introduction to the teory of quadratic forms
  • Theory of multiplicative forms and of Pfister forms
  • The rational admissibility of the triple (r, s, n) and the Hopf condition
  • Some interesting examples of bilinear identities and a theorem of Gabel
  • Artin-Schreier theory of formally real fields
  • Squares and sums of squares in fields and their extension fields
  • Pourchet's theorem that P(Q(X)) = 5 and related results
  • Examples of the Stufe and pythagroas number of fields using the Hasse-Minkowski theorem
  • Reduction of matrices to canonical forms (for Chapter 10)
  • Convex sets (for chaptes 6,7,8,9).