The relative growth rate of the largest partial quotient to the sum of partial quotients in continued fraction expansions

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• 作者：Zhenliang Zhang^a ; ^{zhliang_zhang@163.com" class="auth_mail" title="E-mail the corresponding author} ; Meiying Lü ; ^b ; ^{lmy19831102@hotmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11K55 ; 28A80
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：163
• 期：Complete
• 页码：482-492
• 全文大小：278 K

文摘

In this paper, we mainly study the growth rate of the largest partial quotient relative to the growth rate of the sum of partial quotients for the continued fraction expansion of an irrational number. We establish that the Hausdorff dimension of the set of points with a given relative growth rate is full.