Variations on a theme of Euler
Subtitle: quadratic forms, elliptic curves, and Hopf maps
By: Takashi Ono.
Contributors: Ono, Takashi.
Series: The university series in mathematics; University series in mathematics (Plenum Press)
Publisher: Plenum Press
Published: 1994
Place of publication: New York
Language: eng
Number of pages: 347
Subjects: Forms, Quadratic; Curves, Elliptic; Number theory
Description: In this first-of-its-kind book, Professor Ono postulates that one aspect of classical and modern number theory, including quadratic forms and space elliptic curves as intersections of quadratic surfaces, can be considered as the number theory of Hopf maps.

The text, a translation of Dr. Ono's earlier work, provides a solution to this problem by employing three areas of mathematics: linear algebra, algebraic geometry, and simple algebras. This English-language edition presents a new chapter on arithmetic of quadratic maps, along with an appendix featuring a short survey of subsequent research on congruent numbers by Masanari Kida. The original appendix containing historical and scientific comments on Euler's Elements of Algebra is also included.

Variations on a Theme of Euler is an important reference for researchers and an excellent text for a graduate-level course on number theory.
Notes: Includes bibliographical references and index.
Updated text in English of the 1980 Japanese ed.