no. 1
The metric simultaneous diophantine approximations over formal power series
Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 151-161.

Nous étudions les propriétés métriques de l'approximation diophantienne simultanée dans le cas non archimédien. Nous prouvons d'abord une loi du 0 - 1 de type Gallagher, que nous utilisons ensuite pour obtenir un résultat de type Duffin-Schaeffer.

We discuss the metric theory of simultaneous diophantine approximations in the non-archimedean case. First, we show a Gallagher type 0-1 law. Then by using this theorem, we prove a Duffin-Schaeffer type theorem.

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     title = {The metric simultaneous diophantine approximations over formal power series},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {151--161},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {1},
     year = {2003},
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     zbl = {1045.11052},
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Inoue, Kae. The metric simultaneous diophantine approximations over formal power series. Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 151-161. http://www.numdam.org/item/JTNB_2003__15_1_151_0/

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

[2] G.W. Effinger, D.R. Hayes, Additive Number Theory of Polynomials Over a Finite Field. Oxford University Press, New York, 1991. | MR | Zbl

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

[4] K. Inoue, H. Nakada, On metric Diophantine approximation in positive characteristic, preprint. | MR | Zbl

[5] M.G. Nadkarni, Basic Ergodic Theory. Birkäuser Verlag, Basel-Boston- Berlin, 1991. | MR

[6] A.D. Pollington, R.C. Vaughan, The k-dimensional Duffin and Shaeffer conjecture. Sém. Théor. Nombres Bordeaux 1 (1989), 81-87. | EuDML | Numdam | MR | Zbl

[7] M. Rosen, Number Theory in Function Fields. Springer-Verlag, New York-Berlin-Heidelberg, 2001. | MR | Zbl

[8] V.G. Sprindżuk, Metric Theory of Diophantine Approximations. John Wiley & Sons, New York -Toronto-London- Sydney, 1979. | MR | Zbl