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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 Z-number ： ウィキペディア英語版 Mahler's 3/2 problem In mathematics, Mahler's 3/2 problem concerns the existence of "Z-numbers". A Z-number is a real number ''x'' such that the fractional parts :$\backslash left\backslash lbrace\; x\; \backslash left(\backslash frac\; 3\; 2\backslash right)^\; n\; \backslash right\backslash rbrace$ are less than 1/2 for all natural numbers ''n''. Kurt Mahler conjectured in 1968 that there are no Z-numbers. More generally, for a real number α, define Ω(α) as :$\backslash Omega(\backslash alpha)\; =\; \backslash inf\_\backslash theta\backslash left(\backslash right\backslash rbrace\; -\; \backslash liminf\_\; \backslash left\backslash lbrace\backslash right\backslash rbrace\; \}\backslash right).$ Mahler's conjecture would thus imply that Ω(3/2) exceeds 1/2. Flatto, Lagarias, and Pollington showed that :$\backslash Omega\backslash left(\backslash frac\; p\; q\backslash right)\; >\; \backslash frac\; 1\; p$ for rational ''p''/''q''. ==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「Mahler's 3/2 problem」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.