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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Eisenstein reciprocity ： ウィキペディア英語版 Eisenstein reciprocity In algebraic number theory Eisenstein's reciprocity law is a reciprocity law that extends the law of quadratic reciprocity and the cubic reciprocity law to residues of higher powers. It is one of the earliest and simplest of the higher reciprocity laws, and is a consequence of several later and stronger reciprocity laws such as the Artin reciprocity law. It was introduced by , though Jacobi had previously announced (without proof) a similar result for the special cases of 5th, 8th and 12th powers in 1839.〔Lemmermeyer, p. 392.〕 ==Background and notation== Let  $m\; >\; 1$ be an integer, and let   $\backslash mathcal\_m$  be the ring of integers of the ''m''-th cyclotomic field   $\backslash mathbb(\backslash zeta\_m),$  where  $\backslash zeta\_m=e^\}$  is a primitive ''m''-th root of unity. The numbers $\backslash zeta\_m,\; \backslash zeta\_m^2,\backslash dots\backslash zeta\_m^m=1$ are units in $\backslash mathcal\_m.$ (There are other units as well.) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Eisenstein reciprocity」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.