Felipe A. Ram'irez

collaborators

3 papers

math.NT2025

Twisted approximation with restricted denominators

Manuel Hauke, Felipe A. RamÃrez

Given an increasing integer sequence $(a_{n})$ , a real number $I^\pm$ , and a sequence $I ¨ (n)$ , we study the set $W$ of real numbers $I^^{3}$ for which $a_{n} I^\pm - I^^{3}$ is a distance less than $Ï…

math.NT2025

Toward Khintchine's theorem with a moving target: extra divergence or finitely centered target

Gilbert Michaud, Felipe A. RamÃrez

Sz{Ã¼}sz's inhomogeneous version (1958) of Khintchine's theorem (1924) gives conditions on $I ¨ : N \to R_{\geq 0}$ under which for almost every real number $I^\pm$ there…

math.NT2025

General Duffin--Schaeffer-type counterexamples in diophantine approximation

Sam Chow, Manuel Hauke, Andrew Pollington +1

Duffin and Schaeffer provided a famous counterexample to show that Khintchine's theorem fails without monotonicity assumption. Given any monotonically decreasing approximation func…