عنوان

Variations on a Theme of Euler

شابک

9781441932419

شابک

9781475723267

شماره

b402317

عنوان اصلي

Variations on a Theme of Euler

نام عام مواد

[Book]

ساير اطلاعات عنواني

Quadratic Forms, Elliptic Curves, and Hopf Maps /

نام نخستين پديدآور

by Takashi Ono.

محل نشرو پخش و غیره

Boston, MA :

نام ناشر، پخش کننده و غيره

Imprint: Springer,

تاریخ نشرو بخش و غیره

1994.

عنوان فروست

University Series in Mathematics

متن يادداشت

I. Introduction -- 1. Quadratic Forms -- 2. Algebraic Varieties -- 3. Plane Algebraic Curves -- 4. Space Elliptic Curves -- 5. Quadratic Spherical Maps -- 6. Hurwitz Problem -- 7. Arithmetic of Quadratic Maps -- Answers and Hints to Selected Exercises -- A1.4. Chronological Table and Record -- References -- Appendix 2. A Short Survey of Subsequent Research on Congruent Numbers -- Masanari Kida -- References.

بدون عنوان

0

متن يادداشت

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.

شماره استاندارد بين المللي کتاب و موسيقي

9781441932419

عنوان

Springer eBooks

موضوع مستند نشده

Functional analysis.

موضوع مستند نشده

Mathematics.

موضوع مستند نشده

Operator theory.

مستند نام اشخاص تاييد نشده

Ono, Takashi.

مستند نام تنالگان تاييد نشده

SpringerLink (Online service)

تاريخ عمليات

20190307163000.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y