Variations on a Theme of Euler - Quadratic Forms, Elliptic Curves, and Hopf Maps (Paperback, Softcover reprint of hardcover 1st ed. 1995)

The first six chapters and Appendix 1 of this book appeared in Japanese in a book of the same title 15years aga (Jikkyo, Tokyo, 1980).At the request of some people who do not wish to learn Japanese, I decided to rewrite my old work in English. This time, I added a chapter on the arithmetic of quadratic maps (Chapter 7) and Appendix 2, A Short Survey of Subsequent Research on Congruent Numbers, by M. Kida. Some 20 years ago, while rifling through the pages of Selecta Heinz Hopj (Springer, 1964), I noticed a system of three quadratic forms in four variables with coefficientsin Z that yields the map of the 3-sphere to the 2-sphere with the Hopf invariant r =1 (cf. Selecta, p. 52). Immediately I feit that one aspect of classical and modern number theory, including quadratic forms (Pythagoras, Fermat, Euler, and Gauss) and space elliptic curves as intersection of quadratic surfaces (Fibonacci, Fermat, and Euler), could be considered as the number theory of quadratic maps-especially of those maps sending the n-sphere to the m-sphere, i.e., the generalized Hopf maps. Having these in mind, I deliveredseverallectures at The Johns Hopkins University (Topics in Number Theory, 1973-1974, 1975-1976, 1978-1979, and 1979-1980). These lectures necessarily contained the following three basic areas of mathematics: v vi Preface Theta Simple Functions Aigebras Elliptic Curves Number Theory Figure P.l.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	University Series in Mathematics
Release date:	December 2010
First published:	1995
Authors:	Takashi Ono
Dimensions:	229 x 152 x 18mm (L x W x T)
Format:	Paperback
Pages:	347
Edition:	Softcover reprint of hardcover 1st ed. 1995
ISBN-13:	978-1-4419-3241-9
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
LSN:	1-4419-3241-0
Barcode:	9781441932419

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