The Sum-of-Digits-Function and Uniform Distribution Modulo 1

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• 作者：Drmota ; Michael ; Larcher ; Gerhard
• 刊名：Journal of Number Theory
• 出版年：2001
• 期刊代码：78_0022314x
• 类别：mt
• 出版时间：July, 2001
• 卷：89
• 期：1
• 页码：65-96
• 文件大小：210 K

摘要

The aim of this paper is to provide detailed estimates for the discrepancy of the sequences ({α·s_q(n)}) ({x} denotes the fractional part of x) and results concerning the uniform distribution and the discrepancy of the sequences ({α₁·s_q1(n)}, …, {α_d·s_qd(n)}), where α, α₁, …, α_d are fixed irrational numbers and s_q(n) denotes the q-ary sum-of-digits-function.