The sum-of-digits-function and uniform distribution modulo 1

The aim of this paper is to provide detailed estimates for the discrepancy of the sequences ({alpha . s(q)(n)}) ({x} denotes the fractional part of x) and results concerning the uniform distribution and the discrepancy of the sequences ({alpha (1) . s(q1)(n)}, ..., {alpha (d) . s(qd) (n)}), where alpha, alpha (1), ..., alpha (d) are fixed irrational numbers and s(q)(n) denotes the q-ary sum-of-digits-function. (C) zool Academic Press.