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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 Birch's theorem ： ウィキペディア英語版 Birch's theorem In mathematics, Birch's theorem,〔B. J. Birch, ''Homogeneous forms of odd degree in a large number of variables'', Mathematika, 4, pages 102–105 (1957)〕 named for Bryan John Birch, is a statement about the representability of zero by odd degree forms. ==Statement of Birch's theorem== Let ''K'' be an algebraic number field, ''k'', ''l'' and ''n'' be natural numbers, ''r''1, . . . ,''r''''k'' be odd natural numbers, and ''f''1, . . . ,''f''''k'' be homogeneous polynomials with coefficients in ''K'' of degrees ''r''1, . . . ,''r''''k'' respectively in ''n'' variables, then there exists a number ψ(''r''1, . . . ,''r''''k'',''l'',''K'') such that :$n\backslash ge\backslash psi(r\_1,\backslash ldots,r\_k,l,K)$ implies that there exists an ''l''-dimensional vector subspace ''V'' of ''K''''n'' such that :$f\_1(x)=\backslash cdots\; =\; f\_k(x)=0,\backslash quad\backslash forall\; x\backslash in\; V.$ 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「Birch's theorem」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.