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Variations on a Theme of Euler: Quadratic Forms, Elliptic Curves, and Hopf Maps by Takashi Ono (Hardback, 1994)

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Product Information

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 t 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 ticed 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.

Product Identifiers

Publisher
Kluwer Academic Publishers Group, Kluwer Academic / Plenum Publishers
ISBN-10
0306447894
ISBN-13
9780306447891
eBay Product ID (ePID)
95294580

Product Key Features

Author
Takashi Ono
Format
Hardback
Language
English
Subject
Mathematics
Type
Textbook

Dimensions

Weight
1510g
Height
235mm
Width
155mm

Additional Product Features

Place of Publication
Dordrecht
Spine
20mm
Series Title
University Series in Mathematics
Content Note
Biography
Date of Publication
30/11/1994
Genre
Mathematics
Country of Publication
Netherlands

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