Cet article et les suivants de même titre traitent d’un concept nouveau de répartition modulo un, qui apparaît lors de l’étude de certains problèmes de diviseurs tels celui de Dirichlet. La plupart des théorèmes qu’il contient sont établis pour eux-mêmes, cependant que certains d’entre eux permettent d’améliorer diverses applications de la méthode de l’hyperbole de Dirichlet.
This paper and its sequels deal with a new concept of distributions modulo one which is connected with the Dirichlet divisor and similar problems. Each of the theorems has some independent interest, and in addition some of the techniques developed lead to improvements in certain applications of the hyperbola method.
@article{AIF_1976__26_4_115_0,
author = {Saffari, Bahman and Vaughan, R. C.},
title = {On the fractional parts of $x/n$ and related sequences. {I}},
journal = {Annales de l'Institut Fourier},
pages = {115--131},
publisher = {Imprimerie Durand},
address = {Chartres},
volume = {26},
number = {4},
year = {1976},
doi = {10.5802/aif.634},
mrnumber = {56 #2948},
zbl = {0343.10019},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.634/}
}
TY - JOUR AU - Saffari, Bahman AU - Vaughan, R. C. TI - On the fractional parts of $x/n$ and related sequences. I JO - Annales de l'Institut Fourier PY - 1976 SP - 115 EP - 131 VL - 26 IS - 4 PB - Imprimerie Durand PP - Chartres UR - http://www.numdam.org/articles/10.5802/aif.634/ DO - 10.5802/aif.634 LA - en ID - AIF_1976__26_4_115_0 ER -
%0 Journal Article %A Saffari, Bahman %A Vaughan, R. C. %T On the fractional parts of $x/n$ and related sequences. I %J Annales de l'Institut Fourier %D 1976 %P 115-131 %V 26 %N 4 %I Imprimerie Durand %C Chartres %U http://www.numdam.org/articles/10.5802/aif.634/ %R 10.5802/aif.634 %G en %F AIF_1976__26_4_115_0
Saffari, Bahman; Vaughan, R. C. On the fractional parts of $x/n$ and related sequences. I. Annales de l'Institut Fourier, Tome 26 (1976) no. 4, pp. 115-131. doi : 10.5802/aif.634. http://www.numdam.org/articles/10.5802/aif.634/
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[5] and , On the fractional parts of x/n and related sequences, II (to appear). | Numdam | Zbl
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