# On the fractional parts of $x/n$ and related sequences. I

Annales de l'institut Fourier (1976)

- Volume: 26, Issue: 4, page 115-131
- ISSN: 0373-0956

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topSaffari, Bahman, and Vaughan, R. C.. "On the fractional parts of $x/n$ and related sequences. I." Annales de l'institut Fourier 26.4 (1976): 115-131. <http://eudml.org/doc/74296>.

@article{Saffari1976,

abstract = {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.},

author = {Saffari, Bahman, Vaughan, R. C.},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {4},

pages = {115-131},

publisher = {Association des Annales de l'Institut Fourier},

title = {On the fractional parts of $x/n$ and related sequences. I},

url = {http://eudml.org/doc/74296},

volume = {26},

year = {1976},

}

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

PB - Association des Annales de l'Institut Fourier

VL - 26

IS - 4

SP - 115

EP - 131

AB - 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.

LA - eng

UR - http://eudml.org/doc/74296

ER -

## References

top- [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. Zbl0031.25402
- [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. Zbl0032.01601
- [3] L. KUIPERS and H. NIEDERREITER, Uniform distribution of sequences, Wiley, New York, 1974. Zbl0281.10001MR54 #7415
- [4] H. L. MONTGOMERY and R. C. VAUGHAN, Hilbert's inequality, J. London Math. Soc., (2), 8 (1974), 73-82. Zbl0281.10021MR49 #2544
- [5] B. SAFFARI and R. C. VAUGHAN, On the fractional parts of x/n and related sequences, II (to appear). Zbl0379.10023

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