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

Bahman Saffari; R. C. Vaughan

Annales de l'institut Fourier (1976)

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

Abstract

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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.

How to cite

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Saffari, 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

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  1. [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. [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. [3] L. KUIPERS and H. NIEDERREITER, Uniform distribution of sequences, Wiley, New York, 1974. Zbl0281.10001MR54 #7415
  4. [4] H. L. MONTGOMERY and R. C. VAUGHAN, Hilbert's inequality, J. London Math. Soc., (2), 8 (1974), 73-82. Zbl0281.10021MR49 #2544
  5. [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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