We show that the Duffin and Schaeffer conjecture holds in all dimensions greater than one.
Nous montrons que la conjecture de Duffin et Schaeffer est vraie en toute dimension supérieure à .
Keywords: diophantine approximation, -dimensional, Lebesgues measure, Duffin and Schaeffer conjecture
@article{JTNB_1989__1_1_81_0, author = {A. D. Pollington and R. C. Vaughan}, 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/} }
TY - JOUR TI - The $k$-dimensional Duffin and Schaeffer conjecture JO - Journal de Théorie des Nombres de Bordeaux PY - 1989 DA - 1989/// SP - 81 EP - 88 VL - 1 IS - 1 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.6/ UR - https://zbmath.org/?q=an%3A0714.11048 UR - https://www.ams.org/mathscinet-getitem?mr=1050267 UR - https://doi.org/10.5802/jtnb.6 DO - 10.5802/jtnb.6 LA - en ID - JTNB_1989__1_1_81_0 ER -
A. D. Pollington; R. C. Vaughan. The $k$-dimensional Duffin and Schaeffer conjecture. Journal de Théorie des Nombres de Bordeaux, Volume 1 (1989) no. 1, pp. 81-88. doi : 10.5802/jtnb.6. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.6/
1 Khintchine's problem in metric Diophantine approximation, Duke Math. J. 8 (1941), 243-255. | JFM: 67.0145.03 | MR: 4859 | Zbl: 0025.11002
and ,2 On the distribution of convergents of almost all real numbers, J. Number Theory 2 (1970), 425-441. | MR: 271058 | Zbl: 0205.34902
,3 Approximation by reduced fractions, J. Math. Soc. of Japan 13 (1961), 342-345. | MR: 133297 | Zbl: 0106.04106
,4 Sieve methods," Academic Press, London, 1974. | Zbl: 0298.10026
, "5 Metric theory of Diophantine approximations," V.H. Winston and Sons, Washington D.C., 1979. | Zbl: 0482.10047
, "6 On the metric theory of Diophantine approximation, Pacific J. Math. 76 (1978), 527-539. | MR: 506128 | Zbl: 0352.10026
,7 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
Cited by Sources: