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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 Bloch group ： ウィキペディア英語版 Bloch group In mathematics, the Bloch group is a cohomology group of the Bloch–Suslin complex, named after Spencer Bloch and Andrei Suslin. It is closely related to polylogarithm, hyperbolic geometry and algebraic K-theory. ==Bloch–Wigner function== The dilogarithm function is the function defined by the power series :$$ \operatorname_2(z) = \sum_^\infty . It can be extended by analytic continuation, where the path of integration avoids the cut from 1 to +∞ :$$ \operatorname_2 (z) = -\int_0^z \,\mathrmt. The Bloch–Wigner function is related to dilogarithm function by :$\backslash operatorname\_2\; (z)\; =\; \backslash operatorname\; (\backslash operatorname\_2\; (z)\; )+\backslash arg(1-z)\backslash log|z|$, if $z\; \backslash in\; \backslash mathbb\; \backslash setminus\; \backslash .$ This function enjoys several remarkable properties, e.g. *$\backslash operatorname\_2\; (z)$ is real analytic on $\backslash mathbb\; \backslash setminus\; \backslash .$ *$\backslash operatorname\_2\; (z)\; =\; \backslash operatorname\_2\; \backslash left(1-\backslash frac\backslash right)\; =\; \backslash operatorname\_2\; \backslash left(\backslash frac\backslash right)\; =\; -\; \backslash operatorname\_2\; \backslash left(\backslash frac\backslash right)\; =\; -\backslash operatorname\_2\; (1-z)\; =\; -\backslash operatorname\_2\; \backslash left(\backslash frac\backslash right).$ *$\backslash operatorname\_2\; (x)\; +\; \backslash operatorname\_2\; (y)\; +\; \backslash operatorname\_2\; \backslash left(\backslash frac\backslash right)\; +\; \backslash operatorname\_2\; (1-xy)\; +\; \backslash operatorname\_2\; \backslash left(\backslash frac\backslash right)\; =\; 0.$ The last equation is a variance of Abel's functional equation for the dilogarithm . 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「Bloch group」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.