A reinforcement of the Bourgain-Kontorovich's theorem by elementary methods
Number Theory
2012-07-20 v1
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 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 .
Keywords
Cite
@article{arxiv.1207.4546,
title = {A reinforcement of the Bourgain-Kontorovich's theorem by elementary methods},
author = {Dmitriy Frolenkov and Igor D. Kan},
journal= {arXiv preprint arXiv:1207.4546},
year = {2012}
}
Comments
paper in Russian, summary in English