The summatory function of the sum-of-digits function on polynomial sequences
نویسندگان
چکیده
منابع مشابه
The sum-of-digits function of polynomial sequences
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...
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چکیده ندارد.
15 صفحه اولThe Sum of Digits Function of Squares
We consider the set of squares n2, n < 2k, and split up the sum of binary digits s(n2) into two parts s[<k](n 2) + s[≥k](n 2), where s[<k](n 2) = s(n2 mod 2k) collects the first k digits and s[≥k](n 2) = s(bn2/2kc) collects the remaining digits. We present very precise results on the distribution on s[<k](n 2) and s[≥k](n 2). For example, we provide asymptotic formulas for the numbers #{n < 2k ...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2002
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa104-1-4