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.

@article{JTNB_2003__15_1_151_0,
     author = {Inoue, Kae},
     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},
     doi = {10.5802/jtnb.394},
     zbl = {1045.11052},
     mrnumber = {2019008},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.394/}
}
Kae Inoue. The metric simultaneous diophantine approximations over formal power series. Journal de Théorie des Nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 151-161. doi : 10.5802/jtnb.394. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.394/

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