Abstract.
Let g ≥ 2 be an integer, and let s(n) be the sum of the digits of n in basis g. Let f(n) be a complex valued function defined on positive integers, such that \(\sum_{n\le x} f(n)=o(x)\). We propose sufficient conditions on the function f to deduce the equality \(\sum_{n\le x} f(s(n))=o(x)\). Applications are given, for instance, on the equidistribution mod 1 of the sequence (s(n))α, where α is a positive real number.
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Fouvry, E. Une Remarque sur une Formule Sommatoire liée à la Somme des Chiffres. Mh Math 147, 117–135 (2006). https://doi.org/10.1007/s00605-005-0341-0
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DOI: https://doi.org/10.1007/s00605-005-0341-0