The sum-of-digits function of polynomial sequences

نویسندگان

  • Michael Drmota
  • Christian Mauduit
  • Joël Rivat
چکیده

Let q ≥ 2 be an integer and sq(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 repartition of the sequence (sq(P (n)))n∈N in arithmetic progressions when P ∈ Z[X] is such that P (N) ⊂ N. We answer Gelfond’s question and we show the uniform distribution modulo 1 of the sequence (αsq(P (n)))n∈N for α ∈ R \Q provided that q is a large enough prime number coprime with the leading coefficient of P .

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عنوان ژورنال:
  • J. London Math. Society

دوره 84  شماره 

صفحات  -

تاریخ انتشار 2011