Squares

Many classical and modern results and quadratic forms are brought together in this book. 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. Inhaltsverzeichnis 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.

Product details

• Authors: A. R. Rajwade, A. R. (Panjab University Rajwade, A.r. Rajwade
• Assisted by: J. W. S. Cassels (Editor), N. J. Hitchin (Editor)
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 14.10.1993
• EAN: 9780521426688
• ISBN: 978-0-521-42668-8
• No. of pages: 300
• Series: Cambridge Studies in Italian H
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics