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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 Kronecker symbol ： ウィキペディア英語版 Kronecker symbol In number theory, the Kronecker symbol, written as $\backslash left(\backslash frac\; an\backslash right)$ or $(a|n)$, is a generalization of the Jacobi symbol to all integers $n$. It was introduced by . ==Definition== Let $n$ be a non-zero integer, with prime factorization :$n=u\; \backslash cdot\; p\_1^\; \backslash cdots\; p\_k^,$ where $u$ is a unit (i.e., $u=\backslash pm1$), and the $p\_i$ are primes. Let $a$ be an integer. The Kronecker symbol $(a|n)$ is defined by :$\backslash left(\backslash frac\backslash right)\; =\; \backslash left(\backslash frac\backslash right)\; \backslash prod\_^k\; \backslash left(\backslash frac\backslash right)^.$ For odd $p\_i$, the number $(a|p\_i)$ is simply the usual Legendre symbol. This leaves the case when $p\_i=2$. We define $(a|2)$ by :$\backslash left(\backslash frac\backslash right)\; =$ \begin 0 & \mboxa\mbox \\ 1 & \mbox a \equiv \pm1 \pmod, \\ -1 & \mbox a \equiv \pm3 \pmod. \end Since it extends the Jacobi symbol, the quantity $(a|u)$ is simply $1$ when $u=1$. When $u=-1$, we define it by : Finally, we put : These extensions suffice to define the Kronecker symbol for all integer values $a,n$. Some authors only define the Kronecker symbol for more restricted values; for example, $a$ congruent to $0,1\backslash bmod4$ and $n>0$. 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「Kronecker symbol」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.