Littlewood and Duffin--Schaeffer-type problems in diophantine approximation
Number Theory
2023-08-25 v2
Abstract
Gallagher's theorem describes the multiplicative diophantine approximation rate of a typical vector. We establish a fully-inhomogeneous version of Gallagher's theorem, a diophantine fibre refinement, and a sharp and unexpected threshold for Liouville fibres. Along the way, we prove an inhomogeneous version of the Duffin--Schaeffer conjecture for a class of non-monotonic approximation functions.
Cite
@article{arxiv.2010.09069,
title = {Littlewood and Duffin--Schaeffer-type problems in diophantine approximation},
author = {Sam Chow and Niclas Technau},
journal= {arXiv preprint arXiv:2010.09069},
year = {2023}
}
Comments
83 pages; to appear in the Memoirs of the American Mathematical Society