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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 Teichmüller character ： ウィキペディア英語版 Teichmüller character In number theory, the Teichmüller character ω (at a prime ''p'') is a character of (Z/''q''Z)×, where ''q'' = ''p'' if ''p'' is odd and q=4 if ''p'' = 2, taking values in the roots of unity of the ''p''-adic integers. It was introduced by Oswald Teichmüller. Identifying the roots of unity in the ''p''-adic integers with the corresponding ones in the complex numbers, ω can be considered as a usual Dirichlet character of conductor ''q''. More generally, given a complete discrete valuation ring ''O'' whose residue field ''k'' is perfect of characteristic ''p'', there is a unique multiplicative section of the natural surjection . The image of an element under this map is called its Teichmüller representative. The restriction of ω to ''k''× is called the Teichmüller character. ==Definition== If ''x'' is a ''p''-adic integer, then ω(''x'') is the unique solution of ω(''x'')''p'' = ω(''x'') that is congruent to ''x'' mod ''p''. It can also be defined by :$\backslash omega(x)=\backslash lim\_\; x^$ The multiplicative group of ''p''-adic units is a product of the finite group of roots of unity and a group isomorphic to the ''p''-adic integers. The finite group is cyclic of order ''p'' – 1 or 2, as ''p'' is odd or even, respectively, and so it is isomorphic to (Z/''q''Z)×. The Teichmüller character gives a canonical isomorphism between these two groups. 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「Teichmüller character」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.