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An extension of a theorem of Duffin and Schaeffer in Diophantine approximation

Volume 162 / 2014

Faustin Adiceam Acta Arithmetica 162 (2014), 243-254 MSC: 11J83, 11K60. DOI: 10.4064/aa162-3-3


Duffin and Schaeffer have generalized the classical theorem of Khintchine in metric Diophantine approximation in the case of any error function under the assumption that all the rational approximants are irreducible. This result is extended to the case where the numerators and the denominators of the rational approximants are related by a congruential constraint stronger than coprimality.


  • Faustin AdiceamDepartment of Mathematics
    National University of Ireland at Maynooth
    Maynooth, Co. Kildare, Ireland

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