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

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 1.

DOI : 10.5802/jtnb.6
Keywords: diophantine approximation, $k$-dimensional, Lebesgues measure, Duffin and Schaeffer conjecture 
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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

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

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

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