Faustin Adiceam
Published 2014-08-26Version 1
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.
A Khintchine type theorem for hyperplanes
A transference inequality for rational approximation to points in geometric progression
Rational approximation with generalised $α$-Lüroth expansions
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