The Sum-of-Digits-Function and Uniform Distribution Modulo 1 Original Research Article

The aim of this paper is to provide detailed estimates for the discrepancy of the sequences ({α·sq(n)}) ({x} denotes the fractional part of x) and results concerning the uniform distribution and the discrepancy of the sequences ({α1·sq1(n)}, …, {αd·sqd(n)}), where α, α1, …, αd are fixed irrational numbers and sq(n) denotes the q-ary sum-of-digits-function.