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Let $q \geq 2$ and denote by $s_{q}$ the sum-of-digits function in base $q$ . For $j = 0, 1, \dots, q - 1$ consider $# {0 \leq n < N : s_{q} (2 n) \equiv j (mod q)} .$ In 1983, F. M. Dekking conjectured that this quantity is greater than $N / q$ and, respectively, less than $N / q$ for infinitely many $N$ , thereby claiming an absence of a drift (or Newman) phenomenon. In this paper we prove his conjecture.

On a conjecture of Narkiewicz about functions with non-decreasing normal order

P. D. T. A. Elliott (1976)

Colloquium Mathematicae

On a distribution problem in finite sets

H. G. Meijer, H. Niederreiter (1972)

Compositio Mathematica

On a form of the Erdős-Turán inequality

Jeffrey J. Holt (1996)

Acta Arithmetica

On a Gauss-Kuzmin type problem for piecewise fractional linear maps with explicit invariant measure.

Ganatsiou, C. (2000)

International Journal of Mathematics and Mathematical Sciences

On a metrical theorem of W. Schmidt

V. Bernik (1996)

Acta Arithmetica

On a problem of Alfréd Rényi

Pelegrí Viader, Lluís Bibiloni, Jaume Paradís (1999)

Acta Arithmetica

On a Problem of Erdös in the Theory of Irregularities of Distribution.

József Beck (1987)

Mathematische Annalen

On a problem of K. F. Roth concerning irregularities of point distribution.

J. Beck (1983)

Inventiones mathematicae

On a problem of Narkiewicz concerning uniform distributions of sequences of integers

Alan Zame (1972)

Colloquium Mathematicae

On a problem of R. C. Baker

R. Nair (2003)

Acta Arithmetica

On a problem of Sidon for polynomials over finite fields

Wentang Kuo, Shuntaro Yamagishi (2016)

Acta Arithmetica

Let ω be a sequence of positive integers. Given a positive integer n, we define rₙ(ω) = |(a,b) ∈ ℕ × ℕ : a,b ∈ ω, a+b = n, 0 < a < b|. S. Sidon conjectured that there exists a sequence ω such that rₙ(ω) > 0 for all n sufficiently large and, for all ϵ > 0, $l i m_{n \to \infty} r ₙ (ω) / n^{ϵ} = 0$ . P. Erdős proved this conjecture by showing the existence of a sequence ω of positive integers such that log n ≪ rₙ(ω) ≪ log n. In this paper, we prove an analogue of this conjecture in $_{q} [T]$ , where $_{q}$ is a finite field of q elements....

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Od funkcí periodických ke skoroperiodickým

Odometers and systems of numeration

On a class of arithmetical sets

On a class of uniformly distributed sequences

On a class of weakly almost periodic mappings.

On a conjecture of Dekking : The sum of digits of even numbers

On a conjecture of Narkiewicz about functions with non-decreasing normal order

On a distribution problem in finite sets

On a form of the Erdős-Turán inequality

On a Gauss-Kuzmin type problem for piecewise fractional linear maps with explicit invariant measure.

On a metrical theorem of W. Schmidt

On a problem of Alfréd Rényi

On a Problem of Erdös in the Theory of Irregularities of Distribution.

On a problem of K. F. Roth concerning irregularities of point distribution.

On a problem of Narkiewicz concerning uniform distributions of sequences of integers

On a problem of R. C. Baker

On a problem of Sidon for polynomials over finite fields

On a problem of Tamas Varga

On a problem of W. M. Schmidt concerning one-sided ireegularities of point distrubitions.

On a sequence of (j, ε)-normal approximations to π/4 and the Brouwer conjecture

Currently displaying 1 – 20 of 214