Squares /

• Main Author: Rajwade, A. R.
• Format: Book
• Language: English
• Published: Cambridge, UK : Cambridge University, 1995.
• Series: London Mathematical Society lecture note series ; v. 171
• Subjects: Sums.; Formaly real field.; Number theory.; Field theory.; Sequences.

Table of Contents:

• 1. The theorem of Hurwitz
• 2. The 2n theorems and the Stufe of fields
• 3. Examples of the Stufe of fields and related topics
• 4. Hilbert's 17th problem
• 5. Positive definite functions and sums of squares-- 6. An introduction to Hilbert's theorem
• 7. The two proofs of Hilbert's theorem
• 8. Theorems of Reznick and Choi, Lam and Reznick
• 9. Theorems of Choi, Calderon and Robinson
• 10. The theorem of Hurwitz-Radon
• 11. An introduction to quadratic form theory
• 12. The theory of multiplicative forms and Pfister forms
• 13. The Hopf condition
• 14. Examples of bilinear identities and a theorem of Gabel
• 15. Artin-Schreier theory of formally real fields
• 16. Squares and sums of squares in fields and their extension fields
• 17. Pourchet's theorem and related results
• 18. Examples of the Stufe and Pythagoras number of fields using the Hasse-Minkowski theorem
• Appendix: Reduction of matrices to canonical form.