A converse to linear independence criteria, valid almost everywhere

Stéphane Fischler, Mumtaz Hussain, Simon Kristensen, Jason Levesley

Published 2013-02-08Version 1

We prove a weighted analogue of the Khintchine-Groshev Theorem, where the distance to the nearest integer is replaced by the absolute value. This is subsequently applied to proving the optimality of several linear independence criteria over the field of rational numbers.