5 papers · 1 filter
Duffin--Schaeffer examples, real residue systems, and Bohr-set primes
Stefan M. Hesseling, Felipe A. Ramirez
We prove the following generalization of a well-known result of Duffin and Schaeffer: For any given countable sets and $Z\subset\mathbb{R}\setminus\operatorna…
Independence inheritance and Diophantine approximation for systems of linear forms
Demi Allen, Felipe A. Ramirez
The classical Khintchine-Groshev theorem is a generalization of Khintchine's theorem on simultaneous Diophantine approximation, from approximation of points in to app…
Remarks about inhomogeneous pair correlations
Felipe A. Ramirez
Given an infinite subset , let denote its smallest elements. There is a rich and growing literature on the question of whether for typical $α…
Dirichlet is not just Bad and Singular
Victor Beresnevich, Lifan Guan, Antoine Marnat +2
It is well known that in dimension one the set of Dirichlet improvable real numbers consists precisely of badly approximable and singular numbers. We show that in higher dimensions…
A note on sequences not having metric Poissonian pair correlations
Felipe A. Ramirez
The purpose of this note is to present a construction of sequences which do not have metric Poissonian pair correlations (MPPC) and whose additive energies grow at rates that come…