| 书目名称 | Variations on a Theme of Euler | | 副标题 | Quadratic Forms, Ell | | 编辑 | Takashi Ono | | 视频video | | | 丛书名称 | University Series in Mathematics | | 图书封面 |  | | 描述 | 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- | | 出版日期 | Book 1994 | | 关键词 | Area; DEX; Invariant; algebra; algebraic varieties; arithmetic; elliptic curve; form; functions; mathematics; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4757-2326-7 | | isbn_softcover | 978-1-4419-3241-9 | | isbn_ebook | 978-1-4757-2326-7 | | copyright | Takashi Ono 1994 |
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发表于 2025-3-21 18:40:03
