翻訳と辞書 Words near each other ・ Brauer algebra ・ Brauer College ・ Brauer group ・ Brauer Museum of Art ・ Brauer tree ・ Brauer's burrowing skink ・ Brauer's theorem ・ Brauer's theorem on forms ・ Brauer's theorem on induced characters ・ Brauer's three main theorems ・ Brauerei Ottakringer ・ Brauerei Paderborner ・ Braueriana ・ Brauer–Fowler theorem ・ Brauer–Nesbitt theorem ・ Brauer–Siegel theorem ・ Brauer–Suzuki theorem ・ Brauer–Suzuki–Wall theorem ・ Brauer–Wall group ・ Braughing ・ Braughing Friars ・ Braughing Roman Town ・ Braughing Rural District ・ Braugold ・ Braula ・ Braulidae ・ Braulio ・ Braulio Alonso ・ Braulio Alonso High School ・ Braulio Arellano Domínguez Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Brauer–Siegel theorem ： ウィキペディア英語版 Brauer–Siegel theorem In mathematics, the Brauer–Siegel theorem, named after Richard Brauer and Carl Ludwig Siegel, is an asymptotic result on the behaviour of algebraic number fields, obtained by Richard Brauer and Carl Ludwig Siegel. It attempts to generalise the results known on the class numbers of imaginary quadratic fields, to a more general sequence of number fields :$K\_1,\; K\_2,\; \backslash ldots.\backslash$ In all cases other than the rational field Q and imaginary quadratic fields, the regulator ''R''''i'' of ''K''''i'' must be taken into account, because ''K''i then has units of infinite order by Dirichlet's unit theorem. The quantitative hypothesis of the standard Brauer–Siegel theorem is that if ''D''''i'' is the discriminant of ''K''''i'', then : $\backslash frac\; \backslash to\; 0\backslash texti\; \backslash to\backslash infty.$ Assuming that, and the algebraic hypothesis that ''K''''i'' is a Galois extension of Q, the conclusion is that : $\backslash frac\; \backslash to\; 1\backslash texti\; \backslash to\backslash infty$ where ''h''''i'' is the class number of ''K''''i''. This result is ineffective, as indeed was the result on quadratic fields on which it built. Effective results in the same direction were initiated in work of Harold Stark from the early 1970s. ==References== * Richard Brauer, ''On the Zeta-Function of Algebraic Number Fields'', ''American Journal of Mathematics'' 69 (1947), 243–250. 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「Brauer–Siegel 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.