ALPHA-EXPANSIONS, LINEAR RECURRENCES, AND THE SUM-OF-DIGITS FUNCTION

被引：19

作者：

GRABNER, PJ ^{[1
]}

TICHY, RF ^{[1
]}

机构：

[1] GRAZ TECH UNIV,INST MATH,A-8010 GRAZ,AUSTRIA

来源：

MANUSCRIPTA MATHEMATICA | 1991年 / 70卷 / 03期

关键词：

REPRESENTATION;

D O I：

10.1007/BF02568381

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a generalization of the ordinary q-ary digit expansion of positive integers to arbitrary real bases alpha > 1. We investigate the properties of the sum-of-digit function s(n). We give an asymptotic formula for the sum SIGMA-n < N(s(n)) and consider the distribution properties of the sequence xs(n) for irrational x.

引用

页码：311 / 324

页数：14

共 21 条

[1]

Brauer A, 1951, MATH NACHR, V4, P250

[2] REPRESENTATION OF NATURAL INTEGERS AND STATISTICAL INDEPENDANCE-2 [J].