On the discrepancy of sequences associated with the sum-of-digits function

Larcher, Gerhard, et al. "On the discrepancy of sequences associated with the sum-of-digits function." Annales de l'institut Fourier 37.3 (1987): 1-17. <http://eudml.org/doc/74765>.

@article{Larcher1987,
abstract = {If $w=(q_k)_\{k\in \{\bf N\}\}$ denotes the sequence of best approximation denominators to a real $\alpha $, and $s_\alpha (n)$ denotes the sum of digits of $n$ in the digit representation of $n$ to base $w$, then for all $x$ irrational, the sequence $(s_\alpha (n)\cdot x)_\{n\in \{\bf N\}\}$ is uniformly distributed modulo one. Discrepancy estimates for the discrepancy of this sequence are given, which turn out to be best possible if $\alpha $ has bounded continued fraction coefficients.},
author = {Larcher, Gerhard, Kopecek, N., Tichy, R. F., Turnwald, G.},
journal = {Annales de l'institut Fourier},
keywords = {uniform distribution; sum-of-digits function; digit representation; discrepancy},
language = {eng},
number = {3},
pages = {1-17},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the discrepancy of sequences associated with the sum-of-digits function},
url = {http://eudml.org/doc/74765},
volume = {37},
year = {1987},
}

TY - JOUR
AU - Larcher, Gerhard
AU - Kopecek, N.
AU - Tichy, R. F.
AU - Turnwald, G.
TI - On the discrepancy of sequences associated with the sum-of-digits function
JO - Annales de l'institut Fourier
PY - 1987
PB - Association des Annales de l'Institut Fourier
VL - 37
IS - 3
SP - 1
EP - 17
AB - If $w=(q_k)_{k\in {\bf N}}$ denotes the sequence of best approximation denominators to a real $\alpha $, and $s_\alpha (n)$ denotes the sum of digits of $n$ in the digit representation of $n$ to base $w$, then for all $x$ irrational, the sequence $(s_\alpha (n)\cdot x)_{n\in {\bf N}}$ is uniformly distributed modulo one. Discrepancy estimates for the discrepancy of this sequence are given, which turn out to be best possible if $\alpha $ has bounded continued fraction coefficients.
LA - eng
KW - uniform distribution; sum-of-digits function; digit representation; discrepancy
UR - http://eudml.org/doc/74765
ER -