Geodesic
ON BADLY APPROXIMABLE COMPLEX NUMBERS
Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 349-355

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DOI

We show that the set of complex numbers which are badly approximable by ratios of elements of the ring of integers in , where D ∈ {1, 2, 3, 7, 11, 19, 43, 67, 163} has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably regular fractal set.
DOI : 10.1017/S0017089510000042
Mots-clés : 11J83 
ESDAHL-SCHOU, R.; KRISTENSEN, S. ON BADLY APPROXIMABLE COMPLEX NUMBERS. Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 349-355. doi: 10.1017/S0017089510000042
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     author = {ESDAHL-SCHOU, R. and KRISTENSEN, S.},
     title = {ON {BADLY} {APPROXIMABLE} {COMPLEX} {NUMBERS}},
     journal = {Glasgow mathematical journal},
     pages = {349--355},
     year = {2010},
     volume = {52},
     number = {2},
     doi = {10.1017/S0017089510000042},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000042/}
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