| SYMMETRIC AND ASYMMETRIC DIOPHANTINE APPROXIMATION |
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| 作者姓名： | TONG Jingcheng |
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| 作者单位： | TONG Jingcheng Department of Mathematics and Statistics，University of North Florida，Jacksonville，FL 32224，USA. |
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| 摘 要： | §1. Introduction Let ξbe an irrational number with simple continued fraction expansion ξ= a0;a1,···,ai,···]and pi be its ith convergent. In 1], the present author considered the well-known inequality q
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| 关 键 词： | DIOPHANTINE近似 连续分数式 无理数 收敛性 |
| 收稿时间： | 5/3/2012 12:00:00 AM |
SYMMETRIC AND ASYMMETRIC DIOPHANTINE APPROXIMATION |
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| TONG Jingcheng.SYMMETRIC AND ASYMMETRIC DIOPHANTINE APPROXIMATION[J].Chinese Annals of Mathematics,Series B,2004,25(1):139-142. |
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| Authors: | TONG Jingcheng |
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| Institution: | Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL 32224, USA |
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| Abstract: | Let ξ be an irrational number with simple continued fraction expansion ξ= a0;a1,… ,ai,…] and pi/qi be its ith convergent. Let Ci be defined by ξ - pi/qi = (-1)i/(Ciqiqi+1). The author proves the following theorem: Theorem. Let r ＞ 1, R ＞ 1 be two real numbers and L=1/r-1+1/R-1 +annan+1rR, K=1/2(L+ L2-4/(r-1)(R-1)). Then (i) Cn-2 ＜r, Cn ＜R imply Cn-1 ＞K; (ii) Cn-2 ＞r, Cn ＞R imply Cn-1 ＜K. This theorem generalizes the main result in 1]. |
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| Keywords: | Diophantine approximation Simple continued fraction expansion |
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