6 citations · 15 across the 7 of their papers we have counts for
8 papers
Counterexamples to the inhomogeneous Duffin-Schaeffer Conjecture
Manuel Hauke-Treuer, James Maynard, Andrew Pollington
The Duffin-Schaeffer Conjecture, proven in 2020, gives a zero-full dichotomy for the approximation of irrational numbers with reduced fractions for arbitrary approximation function…
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…
Simultaneous visibility in the integer lattice
Daniel Berend, Rishi Kumar, Andrew Pollington
Two lattice points are visible from one another if there is no lattice point on the open line segment joining them. Let be a finite subset of . The asymptotic den…
Inhomogeneous Diophantine Approximation on -sets with restricted denominators
Andrew D. Pollington, Sanju Velani, Agamemnon Zafeiropoulos +1
Let be a set that supports a probability measure with the property that for some constant . Let $\mathcal{A}=…
The Inhomogeneous Hall's Ray
D. J. Crisp, W. Moran, A. D. Pollington
We show that the inhomogenous approximation spectrum, associated to an irrational number α always has a Hall's Ray; that is, there is an ε>0 such that [0,ε) is a subset of the spec…
On a problem in simultaneous Diophantine approximation: Schmidt's conjecture
Dzmitry Badziahin, Andrew Pollington, Sanju Velani
For any with , let $\bad(i,j)$ denote the set of points for which for all . Here $c…