On a theorem of V. Bernik in the metric theory of Diophantine approximation
V. Beresnevich (2005)
Acta Arithmetica
Similarity:
V. Beresnevich (2005)
Acta Arithmetica
Similarity:
Kae Inoue, Hitoshi Nakada (2003)
Acta Arithmetica
Similarity:
Simon Kristensen (2006)
Acta Arithmetica
Similarity:
Dong Han Kim, Hitoshi Nakada (2011)
Acta Arithmetica
Similarity:
Victor Beresnevich, Sanju Velani (2008)
Acta Arithmetica
Similarity:
Faustin Adiceam (2014)
Acta Arithmetica
Similarity:
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.
Victor Beresnevich, Alan Haynes, Sanju Velani (2013)
Acta Arithmetica
Similarity:
We develop the classical theory of Diophantine approximation without assuming monotonicity or convexity. A complete 'multiplicative' zero-one law is established akin to the 'simultaneous' zero-one laws of Cassels and Gallagher. As a consequence we are able to establish the analogue of the Duffin-Schaeffer theorem within the multiplicative setup. The key ingredient is the rather simple but nevertheless versatile 'cross fibering principle'. In a nutshell it enables us to 'lift' zero-one...
M.M. Dodson (1992)
Journal für die reine und angewandte Mathematik
Similarity:
Gerhard Larcher (1997)
Manuscripta mathematica
Similarity:
Jan Florek (2008)
Acta Arithmetica
Similarity:
Michael Fuchs, Dong Han Kim (2016)
Acta Arithmetica
Similarity:
We give a necessary and sufficient condition such that, for almost all s ∈ ℝ, ||nθ - s|| < ψ(n) for infinitely many n ∈ ℕ, where θ is fixed and ψ(n) is a positive, non-increasing sequence. This can be seen as a dual result to classical theorems of Khintchine and Szüsz which dealt with the situation where s is fixed and θ is random. Moreover, our result contains several earlier ones as special cases: two old theorems of Kurzweil, a theorem of Tseng...
Charles Osgood (1969)
Acta Arithmetica
Similarity:
Charles Osgood (1969)
Acta Arithmetica
Similarity:
Vitaly Bergelson, Inger J. Håland Knutson, Randall McCutcheon (2005)
Acta Arithmetica
Similarity: