Comme promis dans l’article no I de même titre (Ann. Inst. Fourier, 26-4 (1976), 115-131), nous étudions ici la répartition asymptotique des parties fractionnaires de où est une fonction arithmétique (à savoir , , ) et un entier (ou un nombre premier) parcourant l’intervalle . On s’est efforcé de démontrer des formes assez fines des théorèmes, encore que certains résultats se prêtent à des améliorations au prix d’une technicité accrue. Des applications arithmétiques seront données plus tard.
As promised in the first paper of this series (Ann. Inst. Fourier, 26-4 (1976), 115-131), these two articles deal with the asymptotic distribution of the fractional parts of where is an arithmetical function (namely , , ) and is an integer (or a prime order) running over the interval . The results obtained are rather sharp, although one can improve on some of them at the cost of increased technicality. Number-theoretic applications will be given later on.
@article{AIF_1977__27_2_1_0,
author = {Saffari, Bahman and Vaughan, R. C.},
title = {On the fractional parts of $x/n$ and related sequences. {II}},
journal = {Annales de l'Institut Fourier},
pages = {1--30},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {27},
number = {2},
year = {1977},
doi = {10.5802/aif.649},
mrnumber = {58 #554a},
zbl = {0379.10023},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.649/}
}
TY - JOUR AU - Saffari, Bahman AU - Vaughan, R. C. TI - On the fractional parts of $x/n$ and related sequences. II JO - Annales de l'Institut Fourier PY - 1977 SP - 1 EP - 30 VL - 27 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.649/ DO - 10.5802/aif.649 LA - en ID - AIF_1977__27_2_1_0 ER -
%0 Journal Article %A Saffari, Bahman %A Vaughan, R. C. %T On the fractional parts of $x/n$ and related sequences. II %J Annales de l'Institut Fourier %D 1977 %P 1-30 %V 27 %N 2 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.649/ %R 10.5802/aif.649 %G en %F AIF_1977__27_2_1_0
Saffari, Bahman; Vaughan, R. C. On the fractional parts of $x/n$ and related sequences. II. Annales de l'Institut Fourier, Tome 27 (1977) no. 2, pp. 1-30. doi : 10.5802/aif.649. http://www.numdam.org/articles/10.5802/aif.649/
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