Rational approximation and arithmetic progressions

Faustin Adiceam

    Research output: Contribution to journalArticlepeer-review


    A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a metrical and a non-metrical point of view and, on the other hand, from an asymptotic and also a uniform point of view. The principal novelty is a Khintchine type theorem for uniform approximation in this context. Some applications of this theory are also discussed.
    Original languageEnglish
    Pages (from-to)451
    Number of pages486
    JournalInternational Journal of Number Theory
    Issue number2
    Publication statusPublished - 2015


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