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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 Landsberg–Schaar relation ： ウィキペディア英語版 Landsberg–Schaar relation In number theory and harmonic analysis, the Landsberg–Schaar relation (or identity) is the following equation, which is valid for arbitrary positive integers ''p'' and ''q'': :$$ \frac^\exp\left(\frac\right)= \frac}\sum_^\exp\left(-\frac\right). Although both sides are mere finite sums, no proof by entirely finite methods has yet been found. The standard way to prove it〔H. Dym and H.P. McKean. ''Fourier Series and Integrals''. Academic Press, 1972.〕 is to put $\backslash tau=2iq/p+\backslash varepsilon$, where $\backslash varepsilon>0$ in this identity due to Jacobi (which is essentially just a special case of the Poisson summation formula in classical harmonic analysis): :$$ \sum_^e^=\frac^e^ and then let $\backslash varepsilon\backslash to\; 0.$ If we let ''q'' = 1, the identity reduces to a formula for the quadratic Gauss sum modulo ''p''. The Landsberg–Schaar identity can be rephrased more symmetrically as :$$ \frac^\exp\left(\frac\right)= \frac}\sum_^\exp\left(-\frac\right) provided that we add the hypothesis that ''pq'' is an even number. ==References== 〔 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「Landsberg–Schaar relation」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.