The k-dimensional Duffin and Schaeffer conjecture
A. D. Pollington ; R. C. Vaughan
Journal de Théorie des Nombres de Bordeaux, 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.

DOI : https://doi.org/10.5802/jtnb.6
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 = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {81--88},
     publisher = {Universit\'e Bordeaux I},
     volume = {1},
     number = {1},
     year = {1989},
     doi = {10.5802/jtnb.6},
     zbl = {0714.11048},
     mrnumber = {1050267},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.6/}
}
A. D. Pollington; R. C. Vaughan. The $k$-dimensional Duffin and Schaeffer conjecture. Journal de Théorie des Nombres de Bordeaux, Tome 1 (1989) no. 1, pp. 81-88. doi : 10.5802/jtnb.6. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.6/

1 R.J. Duffin and A.C. Schaeffer, Khintchine's problem in metric Diophantine approximation, Duke Math. J. 8 (1941), 243-255. | JFM 67.0145.03 | MR 4859 | Zbl 0025.11002

2 P. Erdös, On the distribution of convergents of almost all real numbers, J. Number Theory 2 (1970), 425-441. | MR 271058 | Zbl 0205.34902

3 P.X. Gallagher, Approximation by reduced fractions, J. Math. Soc. of Japan 13 (1961), 342-345. | MR 133297 | Zbl 0106.04106

4 Halberstam And Richert, "Sieve methods," Academic Press, London, 1974. | Zbl 0298.10026

5 V.G. Sprindzuk, "Metric theory of Diophantine approximations," V.H. Winston and Sons, Washington D.C., 1979. | Zbl 0482.10047

6 J.D. Vaaler, On the metric theory of Diophantine approximation, Pacific J. Math. 76 (1978), 527-539. | MR 506128 | Zbl 0352.10026

7 V.T. Vilchinski, On simultaneous approximations, Vesti Akad Navuk BSSR Ser Fiz.-Mat (1981), 41-47. | Zbl 0464.10040

8, The Duffin and Schaeffer conjecture and simultaneous approximations, Dokl. Akad. Nauk BSSR 25 (1981), 780-783. | MR 631115 | Zbl 0473.10034