Dedekind sums in the vicinity of quadratic irrationals

详细信息	查看全文 | 推荐本文 |

• 作者：Kurt Girstmair ^{kurt.girstmair@uibk.ac.at}
• 关键词：Asymptotic behaviour of Dedekind sums ; Continued fractions of quadratic irrationals
• 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：1788-1792
• 文件大小：110 K

摘要

We study the behaviour of the classical Dedekind sums for convergents of a given quadratic irrational 伪. It turns out that two cases may occur: Either the sequence remains bounded with finitely many cluster points, or tends to +鈭?or 鈭掆垶 like or , respectively. By means of the Barkan-Hickerson-Knuth formula we obtain a precise description of what happens in all cases.