Geodesic
A strengthening of a~theorem of Bourgain and Kontorovich
Izvestiya. Mathematics , Tome 78 (2014) no. 2, pp. 293-353

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We prove that the set of positive integers contains a positive proportion of numbers satisfying Zaremba's conjecture with $A=7$. This result strengthens a similar theorem of Bourgain and Kontorovich obtained for $A=50$.
Keywords: continued fraction, exponential sums.
Mots-clés : continuant 
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     title = {A strengthening of a~theorem of {Bourgain} and {Kontorovich}},
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I. D. Kan; D. A. Frolenkov. A strengthening of a~theorem of Bourgain and Kontorovich. Izvestiya. Mathematics , Tome 78 (2014) no. 2, pp. 293-353. http://geodesic.mathdoc.fr/item/IM2_2014_78_2_a3/