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

2012/07/19 by Dmitriy Frolenkov, Frolenkov, Dmitriy, Игорь Давидович Кан +2
Mathematics · #11J70 #11L05 #11P55 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT #msc:11J70 #msc:11L05 #msc:11P55

paper · pdf · doi:10.48550/arxiv.1207.4546

paper in Russian, summary in English

arxiv created 2012/07/19 · openalex publication_date 2012/07/19 · arxiv updated 2012/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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