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math.NT2026
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…
math.NT2025
Metric bootstraps for limsup sets
Felipe A. Ramirez
In metric Diophantine approximation, one frequently encounters the problem of showing that a limsup set has positive or full measure. Often it is a set of points in -dimensional…
math.NT2024
The Duffin-Schaeffer conjecture with a moving target
Manuel Hauke, Felipe A. Ramirez
We prove the inhomogeneous generalization of the Duffin-Schaeffer conjecture in dimension . That is, given and $Ï:\mathbb{N}\to\mathbb{R}_{\…