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Elliptic Curves : Diophantine Analysis / by S. Lang
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics. ISSN:21969701 ; 231)
版 | 1st ed. 1978. |
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出版者 | (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer) |
出版年 | 1978 |
本文言語 | 英語 |
大きさ | XI, 264 p : online resource |
著者標目 | *Lang, S author SpringerLink (Online service) |
件 名 | LCSH:Mathematical analysis FREE:Analysis |
一般注記 | I. General Algebraic Theory -- I. Elliptic Functions -- II. The Division Equation -- III. p-Adic Addition -- IV. Heights -- V. Kummer Theory -- V1. Integral Points -- II. Approximation of Logarithms -- VII. Auxiliary Results -- VIII. The Baker—Feldman Theorem -- IX. Linear Combinations of Elliptic Logarithms -- X. The Baker—Tijdeman Theorem -- XI. Refined Inequalities It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmetic aspects of the addition formula, over complete fields and over number fields, giving rise to the theory of the height and its quadraticity. We apply this to integral points, covering the inequalities of diophantine approximation both on the multiplicative group and on the elliptic curve directly. Thus the book splits naturally in two parts. The first part deals with the ordinary arithmetic of the elliptic curve: The transcendental parametrization, the p-adic parametrization, points of finite order and the group of rational points, and the reduction of certain diophantine problems by the theory of heights to diophantine inequalities involving logarithms. The second part deals with the proofs of selected inequalities, at least strong enough to obtain the finiteness of integral points HTTP:URL=https://doi.org/10.1007/978-3-662-07010-9 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783662070109 |
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EB00232901 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA299.6-433 DC23:515 |
書誌ID | 4000110704 |
ISBN | 9783662070109 |
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