The sum-of-digits function of canonical number systems: Distribution in residue classes

被引：1
|
作者：
Madritsch, Manfred G. [1 ]
机构：
[1] Graz Univ Technol, Dept Anal & Computat Number Theory, A-8010 Graz, Austria
来源：
JOURNAL OF NUMBER THEORY | 2012年 / 132卷 / 12期
关键词：
Sum of digits; Canonical number system; Exponential sum;
D O I：
10.1016/j.jnt.2012.05.023
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the present paper we investigate the sum-of-digits function for canonical number systems. We are interested in its re-partition in arithmetic progressions and similar results for sum sets. The original problem goes back to Gelfond. who proved the independence of the distribution of the digits and their sum of digits. The present paper extends results by Thuswaldner and Mauduit and Sarkozy to this kind of numeration systems. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：2756 / 2772
页数：17
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