Squares
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Many classical and modern results and quadratic forms are brought together in this book. The treatment is self-contained and of a totally elementary nature requiring only a basic knowledge of rings, fields, polynomials, and matrices, such that the works of Pfister, Hilbert, Hurwitz and others are easily accessible to non-experts and undergraduates alike. The author deals with many different approaches to the study of squares; from the classical works of the late 19th century, to areas of current research. Anyone with an interest in algebra or number theory will find this a most fascinating volume.
Product details
October 1993Paperback
9780521426688
300 pages
228 × 151 × 20 mm
0.393kg
Available
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.
