On Zaremba's Conjecture

2011/07/19 by Jean Bourgain, Bourgain, Jean, Alex Kontorovich +1
Mathematics · #11J70 #11P55 #37D35 #Advanced Topology and Set Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1107.3776

openalex publication_date 2011/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Zaremba's 1971 conjecture predicts that every integer appears as the denominator of a finite continued fraction whose partial quotients are bounded by an absolute constant. We confirm this conjecture for a set of density one.

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