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arXiv · 1207.4546

A reinforcement of the Bourgain-Kontorovich's theorem by elementary methods

Dmitriy Frolenkov·Igor D. Kan
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Abstract

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 conjecture with A=50 has positive proportion in $\N.$ The proof of this theorem is rather complicated and refers to the spectral theory. In this paper,using only elementary methods, the same theorem is proved with A=13 .

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Dmitriy Frolenkov, Igor D. Kan. 2012-07-19. A reinforcement of the Bourgain-Kontorovich's theorem by elementary methods. https://arxiv.org/abs/1207.4546

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