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A functional central limit theorem in Diophantine approximation


Author: Jorge D. Samur
Journal: Proc. Amer. Math. Soc. 111 (1991), 901-911
MSC: Primary 11K60; Secondary 60F17
DOI: https://doi.org/10.1090/S0002-9939-1991-0998739-7
MathSciNet review: 998739
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Abstract: A functional central limit theorem is proved for the number of solutions $ (p,q)$ of the inequality $ \vert q\omega - p\vert < f(q){q^{ - 1}},q \leq n$ (respectively $ 0 < q\omega - p < f(q){q^{ - 1}},q \leq n$ for some functions $ f$ having a positive limit.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-0998739-7
Keywords: Diophantine approximation, functional central limit theorem, invariance principle, continued fraction expansion, mixing random variables
Article copyright: © Copyright 1991 American Mathematical Society

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