Rational approximation and arithmetic progressions

Faustin Adiceam*

*Corresponding author for this work

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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)451-486
Number of pages36
JournalInternational Journal of Number Theory
Issue number2
Publication statusPublished - Mar 2015


  • arithmetic progressions
  • Diophantine approximation
  • metric number theory

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