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On some open problems in Diophantine approximation

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arxiv 1202.4539 v5 pith:HTEE4MUE submitted 2012-02-21 math.NT

Nikolay G. Moshchevitin This is my paper · ORCID
classification math.NT
keywords problemsapproximationdiophantinefamousopensomeconjecturesdiscuss
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We discuss several open problems in Diophantine approximation. Among them there are famous Littlewood's and Zaremba's conjectures as well as some new and not so famous problems.

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  1. On some results of Korobov and Larcher and Zaremba's conjecture

    math.NT 2026-03 accept novelty 7.0 of 10

    Zaremba's conjecture holds for all large primes: an absolute M exists so every large prime p admits a coprime a whose continued-fraction partial quotients are all ≤ M, with quantitative lower bounds on the number of such a.

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