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math.NT2012★ 1 cited
A note on the reinforcement of the Bourgain-Kontorovich's theorem
Dmitriy Frolenkov, Igor D. Kan
Zaremba's conjecture (1971) states that every positive integer number can be represented as a denominator (continuant) of a finite continued fraction $\frac{b}{d}=[d_1,d_2,...,…
math.NT2012★ 6 cited
A reinforcement of the Bourgain-Kontorovich's theorem
Dmitriy Frolenkov, Igor D. Kan
Zaremba's conjecture (1971) states that every positive integer number can be represented as a denominator (continuant) of a finite continued fraction $\frac{b}{d}=[d_1,d_2,...,…
math.NT2012★ 16 cited
A reinforcement of the Bourgain-Kontorovich's theorem by elementary methods
Dmitriy Frolenkov, Igor D. Kan
Recently (in 2011) several new theorems concerning this conjecture were proved by Bourgain and Kontorovich. The easiest of them states that the set of numbers satisfying Zaremba's…