Geodesic
Is Zaremba's conjecture true?
Sbornik. Mathematics, Tome 210 (2019) no. 3, pp. 364-416

Voir la notice de l'article provenant de la source Math-Net.Ru

For finite continued fractions in which all partial quotients lie in the alphabet $\{1,2,3,5\}$, it is shown that the set of denominators not exceeding $N$ has cardinality $\gg N^{0.85}$. A calculation using an analogue of Bourgain-Kontorovich's theorem from 2011 gives $\gg N^{0.80}$. Bibliography: 25 titles.
Keywords: continued fraction, trigonometric sum
Mots-clés : Zaremba's conjecture, partial quotients, continuant, Hausdorff dimension. 
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I. D. Kan. Is Zaremba's conjecture true?. Sbornik. Mathematics, Tome 210 (2019) no. 3, pp. 364-416. http://geodesic.mathdoc.fr/item/SM_2019_210_3_a2/