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math.NT2017
Khintchine's Theorem with random fractions
Felipe A. Ramírez
We prove versions of Khintchine's Theorem (1924) for approximations by rational numbers whose numerators lie in randomly chosen sets of integers, and we explore the extent to which…
math.NT2017★ 2 cited
A characterization of bad approximability
Felipe A. Ramírez
We show that badly approximable vectors are exactly those that cannot, for any inhomogeneous parameter, be inhomogeneously approximated at every monotone divergent rate. This impli…