Metrical Diophantine approximation for quaternions
نویسندگان
چکیده
منابع مشابه
Metrical Diophantine approximation for quaternions
The metrical theory of Diophantine approximation for quaternions is developed using recent results in the general theory. In particular, Quaternionic analogues of the classical theorems of Khintchine, Jarnı́k and Jarnı́k-Besicovitch are established. Introduction Diophantine approximation begins with a more quantitative understanding of the density of the rationals Q in the reals R. The starting p...
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q ψ(q) diverges but A(ψ) is of zero measure. In other words, without the monotonicity assumption, Khintchine’s theorem is false and the famous Duffin-Schaeffer conjecture provides the appropriate statement. The key difference is that in (1), we impose coprimality on the integers p and q. Let A(ψ) denote the resulting subset of A(ψ). The Duffin-Schaeffer conjecture states that the measure of A(ψ...
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2014
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004114000462