Dedekind sums in the vicinity of quadratic irrationals

被引：3
|
作者：
Girstmair, Kurt [1 ]
机构：
[1] Univ Innsbruck, Inst Math, A-6020 Innsbruck, Austria
来源：
JOURNAL OF NUMBER THEORY | 2012年 / 132卷 / 08期
关键词：
Asymptotic behaviour of Dedekind sums; Continued fractions of quadratic irrationals;
D O I：
10.1016/j.jnt.2012.03.008
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the behaviour of the classical Dedekind sums s(m/n) for convergents m/n of a given quadratic irrational alpha. It turns out that two cases may occur: Either the sequence s(m/n) remains bounded with finitely many cluster points, or s(m/n) tends to +infinity or -infinity like + log n or -log n, respectively. By means of the Barkan-Hickerson-Knuth formula we obtain a precise description of what happens in all cases. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：1788 / 1792
页数：5
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