A functional central limit theorem in Diophantine approximation

Samur, Jorge D.

doi:10.1090/S0002-9939-1991-0998739-7

A functional central limit theorem in Diophantine approximation
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Proc. Amer. Math. Soc. 111 (1991), 901-911 Request permission

Abstract:

A functional central limit theorem is proved for the number of solutions $(p,q)$ of the inequality $|q\omega - p| < f(q){q^{ - 1}},q \leq n$ (respectively $0 < q\omega - p < f(q){q^{ - 1}},q \leq n$ for some functions $f$ having a positive limit.

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