no. 4
On the fractional parts of x/n and related sequences. I
Annales de l'Institut Fourier, Tome 26 (1976) no. 4, pp. 115-131.

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.

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     title = {On the fractional parts of $x/n$ and related sequences. {I}},
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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://archive.numdam.org/articles/10.5802/aif.634/

[1] P. Erdös and P. Turán, On a problem in the theory of uniform distributions, I, Proc. Nederl. Acad. Wetensch., 51 (1948), 1146-1154, Indagationes Math., 10 (1948), 370-378. | Zbl

[2] P. Erdös and P. Turán, On a problem in the theory of uniform distribution, II, Proc. Nederl. Acad. Wetensch., 51 (1948), 1262-1269, Indagationes Math., 10 (1948), 406-413. | Zbl

[3] L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Wiley, New York, 1974. | MR | Zbl

[4] H. L. Montgomery and R. C. Vaughan, Hilbert's inequality, J. London Math. Soc., (2), 8 (1974), 73-82. | MR | Zbl

[5] B. Saffari and R. C. Vaughan, On the fractional parts of x/n and related sequences, II (to appear). | Numdam | Zbl

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