no. 3
Simultaneous Diophantine approximation with a divisibility condition
Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 3, pp. 987-1008

In a previous paper ([9]), we studied certain sequences of simultaneous rational approximations in ℝ 2 which present some analogy with the continued fractions. We got results around the Littlewood conjecture by using such approximations. Here we show that these results also hold when we add divisibility conditions.

Dans un article précédent ([9]), nous étudiions des approximations rationnelles simultanées dans ℝ 2 qui présentent une certaine analogie avec les fractions continues. Nous obtenions des résultats autour de la conjecture de Littlewood en utilisant de telles approximations. Nous montrons ici que ces résultats restent vrais si l’on ajoute des conditions de divisibilité.

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DOI : 10.5802/jtnb.1303
Classification : 11J13, 11J68
Keywords: Littlewood conjecture. Simultaneous Diophantine approximation. Divisibility.
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Simultaneous {Diophantine} approximation with a divisibility condition},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {987--1008},
     year = {2024},
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Mathan, Bernard de. Simultaneous Diophantine approximation with a divisibility condition. Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 3, pp. 987-1008. doi: 10.5802/jtnb.1303

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