The k -dimensional Duffin and Schaeffer conjecture

A. D. Pollington; R. C. Vaughan

Journal de théorie des nombres de Bordeaux (1989)

  • Volume: 1, Issue: 1, page 81-88
  • ISSN: 1246-7405

Abstract

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We show that the Duffin and Schaeffer conjecture holds in all dimensions greater than one.

How to cite

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Pollington, A. D., and Vaughan, R. C.. "The $k$-dimensional Duffin and Schaeffer conjecture." Journal de théorie des nombres de Bordeaux 1.1 (1989): 81-88. <http://eudml.org/doc/93503>.

@article{Pollington1989,
abstract = {We show that the Duffin and Schaeffer conjecture holds in all dimensions greater than one.},
author = {Pollington, A. D., Vaughan, R. C.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {diophantine approximation; $k$-dimensional; Lebesgues measure; Duffin and Schaeffer conjecture; metric Diophantine approximation; higher-dimensional analogue; Duffin-Schaeffer conjecture; inequalities},
language = {eng},
number = {1},
pages = {81-88},
publisher = {Université Bordeaux I},
title = {The $k$-dimensional Duffin and Schaeffer conjecture},
url = {http://eudml.org/doc/93503},
volume = {1},
year = {1989},
}

TY - JOUR
AU - Pollington, A. D.
AU - Vaughan, R. C.
TI - The $k$-dimensional Duffin and Schaeffer conjecture
JO - Journal de théorie des nombres de Bordeaux
PY - 1989
PB - Université Bordeaux I
VL - 1
IS - 1
SP - 81
EP - 88
AB - We show that the Duffin and Schaeffer conjecture holds in all dimensions greater than one.
LA - eng
KW - diophantine approximation; $k$-dimensional; Lebesgues measure; Duffin and Schaeffer conjecture; metric Diophantine approximation; higher-dimensional analogue; Duffin-Schaeffer conjecture; inequalities
UR - http://eudml.org/doc/93503
ER -

References

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  1. 1 R.J. Duffin and A.C. Schaeffer, Khintchine's problem in metric Diophantine approximation, Duke Math. J.8 (1941), 243-255. Zbl0025.11002MR4859JFM67.0145.03
  2. 2 P. Erdös, On the distribution of convergents of almost all real numbers, J. Number Theory2 (1970), 425-441. Zbl0205.34902MR271058
  3. 3 P.X. Gallagher, Approximation by reduced fractions, J. Math. Soc. of Japan13 (1961), 342-345. Zbl0106.04106MR133297
  4. 4 Halberstam and Richert, "Sieve methods," Academic Press, London, 1974. Zbl0298.10026
  5. 5 V.G. Sprindzuk, "Metric theory of Diophantine approximations," V.H. Winston and Sons, Washington D.C., 1979. Zbl0482.10047
  6. 6 J.D. Vaaler, On the metric theory of Diophantine approximation, Pacific J. Math.76 (1978), 527-539. Zbl0352.10026MR506128
  7. 7 V.T. Vilchinski, On simultaneous approximations, Vesti Akad Navuk BSSR Ser Fiz.-Mat (1981), 41-47. Zbl0464.10040
  8. 8, The Duffin and Schaeffer conjecture and simultaneous approximations, Dokl. Akad. Nauk BSSR25 (1981), 780-783. Zbl0473.10034MR631115

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