A variational principle in the parametric geometry of numbers, with applications to metric Diophantine approximation
Sign Up to like & getrecommendations! Published in 2017 at "Comptes Rendus Mathematique"
DOI: 10.1016/j.crma.2017.07.007
Abstract: Abstract We establish a new connection between metric Diophantine approximation and the parametric geometry of numbers by proving a variational principle facilitating the computation of the Hausdorff and packing dimensions of many sets of interest… read more here.
Keywords: diophantine approximation; parametric geometry; metric diophantine; geometry ... See more keywords
Variants of Khintchine's theorem in metric Diophantine approximation
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2020.01.005
Abstract: New results towards the Duffin-Schaeffer conjecture, which is a fundamental unsolved problem in metric number theory, have been established recently assuming extra divergence. Given a non-negative function $\psi: \mathbb{N}\to\mathbb{R}$ we denote by $W(\psi)$ the set… read more here.
Keywords: variants khintchine; psi; diophantine approximation; theorem metric ... See more keywords