Rational approximation and arithmetic progressions

Faustin Adiceam

doi:10.1142/S1793042115500232

Rational approximation and arithmetic progressions

Faustin Adiceam^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	451-486
Number of pages	36
Journal	International Journal of Number Theory
Volume	11
Issue number	2
DOIs	https://doi.org/10.1142/S1793042115500232
Publication status	Published - Mar 2015

Keywords

arithmetic progressions
Diophantine approximation
metric number theory

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10.1142/S1793042115500232

Cite this

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Rational approximation and arithmetic progressions

Abstract

Keywords

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