Explicit irrationality measures for continued fractions

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• 作者：Jaroslav Han膷l^a ; ¹ ; ^hancl@osu.cz ; Marko Leinonen^b ; ² ; Kalle Lepp&auml ; l&auml ; ^b ; ³ ; Tapani Matala-aho^b ; ⁴ ; ^{tapani.matala-aho@oulu.fi}
• 关键词：Measure of irrationality ; Napier始s constant ; Nested logarithm fraction ; Simple continued fraction
• 刊名：Journal of Number Theory
• 出版年：2012
• 期刊代码：78_0022314x
• 类别：mt
• 出版时间：August, 2012
• 卷：132
• 期：8
• 页码：1758-1769
• 文件大小：151 K

摘要

Let , , , , be a simple continued fraction determined by an infinite integer sequence . We are interested in finding an effective irrationality measure as explicit as possible for the irrational number 蟿. In particular, our interest is focused on sequences with an upper bound at most , where and . In addition to our main target, arithmetic of continued fractions, we shall pay special attention to studying the nature of the inverse function of .