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Article Dans Une Revue Journal of the London Mathematical Society Année : 2011

The sum-of-digits function of polynomial sequences

Résumé

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 re-partition of the sequence (sq(P(n)))n∈ in arithmetic progressions when P∈[XŞ is such that P()⊂. We answer Gelfond's question and we show the uniform distribution modulo 1 of the sequence ( sq(P(n)))n∈ for ∈ , provided that q is a large enough prime number co-prime with the leading coefficient of P.

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Dates et versions

hal-01260110 , version 1 (21-01-2016)

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Michael Drmota, Christian Mauduit, Joël Rivat. The sum-of-digits function of polynomial sequences. Journal of the London Mathematical Society, 2011, 84 (1), pp.81-102. ⟨10.1112/jlms/jdr003⟩. ⟨hal-01260110⟩
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