Geodesic
A~strengthening of a~theorem of Bourgain and Kontorovich. III
Izvestiya. Mathematics , Tome 79 (2015) no. 2, pp. 288-310

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We prove that the set of positive integers contains a positive proportion of denominators of the finite continued fractions all of whose partial quotients belong to the alphabet $\{1,2,3,4,10\}$. The corresponding theorem was previousy known only for the alphabet $\{1,2,3,4,5\}$ and for alphabets of larger cardinality.
Keywords: continued fraction, trigonometric sum
Mots-clés : continuant, Zaremba's conjecture. 
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     author = {I. D. Kan},
     title = {A~strengthening of a~theorem of {Bourgain} and {Kontorovich.} {III}},
     journal = {Izvestiya. Mathematics },
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I. D. Kan. A~strengthening of a~theorem of Bourgain and Kontorovich. III. Izvestiya. Mathematics , Tome 79 (2015) no. 2, pp. 288-310. http://geodesic.mathdoc.fr/item/IM2_2015_79_2_a3/