2014/06/25 by Faustin Adiceam
Computer Science · Mathematics · #Approximation Theory and Sequence Spaces #Asymptotic formula #Diophantine approximation #Irrational number #Mathematical Dynamics and Fractals #Novelty #Point (geometry) #Rational number #Type (biology) #math.NT #msc:11J83 #msc:11K60 #semigroups and automata theory
paper · pdf · doi:10.1142/s1793042115500232
openalex publication_date 2014/06/25 · arxiv created 2014/08/26 · arxiv updated 2014/08/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.