2 citations · 2 across the 4 of their papers we have counts for
7 papers
The inhomogeneous Khintchine Theorem in dimension two
Demi Allen, Manuel Hauke-Treuer, Felipe A. Ramírez
We prove that the inhomogeneous variant of Khintchine's Theorem holds in dimension without any monotonicity assumption. This resolves the last remaining case in the metric theo…
Approximation by random fractions
Laima Kaziulytė, Felipe A. Ramírez
We study approximation in the unit interval by rational numbers whose numerators are selected randomly with certain probabilities. Previous work showed that an analogue of Khintchi…
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…
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…
Metric Diophantine Approximation: aspects of recent work
Victor Beresnevich, Felipe Ramírez, Sanju Velani
In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approximation; such as theorems of Khintchine, Jarn\'ık, Duffin-Schaeffer and Gallagher.…
Rational approximation of affine coordinate subspaces of Euclidean space
Felipe A. Ramírez, David S. Simmons, Fabian Süess
We show that affine coordinate subspaces of dimension at least two in Euclidean space are of Khintchine type for divergence. For affine coordinate subspaces of dimension one, we pr…
Khintchine types of translated coordinate hyperplanes
Felipe A. Ramírez
There has been great interest in developing a theory of "Khintchine types" for manifolds embedded in Euclidean space, and considerable progress has been made for curved manifolds.…