The k-dimensional Duffin and Schaeffer conjecture
Séminaire de théorie des nombres de Bordeaux, Série 2, Tome 1 (1989) no. 1, pp. 81-88.

Nous montrons que la conjecture de Duffin et Schaeffer est vraie en toute dimension supérieure à 1.

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

Mots-clés : diophantine approximation, $k$-dimensional, Lebesgues measure, Duffin and Schaeffer conjecture 
@article{JTNB_1989__1_1_81_0,
     author = {Pollington, A. D. and Vaughan, R. C.},
     title = {The $k$-dimensional {Duffin} and {Schaeffer} conjecture},
     journal = {S\'eminaire de th\'eorie des nombres de Bordeaux},
     pages = {81--88},
     publisher = {Universit\'e Bordeaux I},
     volume = {Ser. 2, 1},
     number = {1},
     year = {1989},
     mrnumber = {1050267},
     zbl = {0714.11048},
     language = {en},
     url = {http://archive.numdam.org/item/JTNB_1989__1_1_81_0/}
}
TY  - JOUR
AU  - Pollington, A. D.
AU  - Vaughan, R. C.
TI  - The $k$-dimensional Duffin and Schaeffer conjecture
JO  - Séminaire de théorie des nombres de Bordeaux
PY  - 1989
SP  - 81
EP  - 88
VL  - 1
IS  - 1
PB  - Université Bordeaux I
UR  - http://archive.numdam.org/item/JTNB_1989__1_1_81_0/
LA  - en
ID  - JTNB_1989__1_1_81_0
ER  - 
%0 Journal Article
%A Pollington, A. D.
%A Vaughan, R. C.
%T The $k$-dimensional Duffin and Schaeffer conjecture
%J Séminaire de théorie des nombres de Bordeaux
%D 1989
%P 81-88
%V 1
%N 1
%I Université Bordeaux I
%U http://archive.numdam.org/item/JTNB_1989__1_1_81_0/
%G en
%F JTNB_1989__1_1_81_0
Pollington, A. D.; Vaughan, R. C. The $k$-dimensional Duffin and Schaeffer conjecture. Séminaire de théorie des nombres de Bordeaux, Série 2, Tome 1 (1989) no. 1, pp. 81-88. http://archive.numdam.org/item/JTNB_1989__1_1_81_0/

1 R.J. Duffin and A.C. Schaeffer, Khintchine's problem in metric Diophantine approximation, Duke Math. J. 8 (1941), 243-255. | JFM | MR | Zbl

2 P. Erdös, On the distribution of convergents of almost all real numbers, J. Number Theory 2 (1970), 425-441. | MR | Zbl

3 P.X. Gallagher, Approximation by reduced fractions, J. Math. Soc. of Japan 13 (1961), 342-345. | MR | Zbl

4 Halberstam And Richert, "Sieve methods," Academic Press, London, 1974. | Zbl

5 V.G. Sprindzuk, "Metric theory of Diophantine approximations," V.H. Winston and Sons, Washington D.C., 1979. | Zbl

6 J.D. Vaaler, On the metric theory of Diophantine approximation, Pacific J. Math. 76 (1978), 527-539. | MR | Zbl

7 V.T. Vilchinski, On simultaneous approximations, Vesti Akad Navuk BSSR Ser Fiz.-Mat (1981), 41-47. | Zbl

8, The Duffin and Schaeffer conjecture and simultaneous approximations, Dokl. Akad. Nauk BSSR 25 (1981), 780-783. | MR | Zbl