科研之友
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摘要
Let q >= 2 be an integer and s(q)(n) denote the sum of the digits in base q of the positive integer n. The goal of this work is to study a problem of Gelfond concerning the re-partition of the sequence (s(q)(P(n)))(n is an element of N) in arithmetic progressions when P is an element of Z[X] is such that P(N)subset of N. We answer Gelfond's question and we show the uniform distribution modulo 1 of the sequence (alpha s(q)(P(n)))(n is an element of N) for alpha is an element of R\Q, provided that q is a large enough prime number co-prime with the leading coefficient of P.
- 出版日期2011-8
