If denotes the sequence of best approximation denominators to a real , and denotes the sum of digits of in the digit representation of to base , then for all irrational, the sequence is uniformly distributed modulo one. Discrepancy estimates for the discrepancy of this sequence are given, which turn out to be best possible if has bounded continued fraction coefficients.
Soit le développement en fraction continue du nombre irrationnel ; soit la suite de dénominateur des réduites successives de . Tout entier naturel se développe de manière unique sous la forme est la somme de chiffres de . La suite est équirépartie modulo 1 si est irrationnel. Nous prouvons quelques estimations de la discrépance de la suite .
@article{AIF_1987__37_3_1_0, author = {Larcher, Gerhard and Kopecek, N. and Tichy, R. F. and Turnwald, G.}, title = {On the discrepancy of sequences associated with the sum-of-digits function}, journal = {Annales de l'Institut Fourier}, pages = {1--17}, publisher = {Imprimerie Louis-Jean}, address = {Gap}, volume = {37}, number = {3}, year = {1987}, doi = {10.5802/aif.1095}, mrnumber = {89c:11119}, zbl = {0601.10038}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1095/} }
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 SP - 1 EP - 17 VL - 37 IS - 3 PB - Imprimerie Louis-Jean PP - Gap UR - http://archive.numdam.org/articles/10.5802/aif.1095/ DO - 10.5802/aif.1095 LA - en ID - AIF_1987__37_3_1_0 ER -
%0 Journal Article %A Larcher, Gerhard %A Kopecek, N. %A Tichy, R. F. %A Turnwald, G. %T On the discrepancy of sequences associated with the sum-of-digits function %J Annales de l'Institut Fourier %D 1987 %P 1-17 %V 37 %N 3 %I Imprimerie Louis-Jean %C Gap %U http://archive.numdam.org/articles/10.5802/aif.1095/ %R 10.5802/aif.1095 %G en %F AIF_1987__37_3_1_0
Larcher, Gerhard; Kopecek, N.; Tichy, R. F.; Turnwald, G. On the discrepancy of sequences associated with the sum-of-digits function. Annales de l'Institut Fourier, Volume 37 (1987) no. 3, pp. 1-17. doi : 10.5802/aif.1095. http://archive.numdam.org/articles/10.5802/aif.1095/
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