A converse to linear independence criteria, valid almost everywhere
Number Theory
2013-02-11 v1
Abstract
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.
Cite
@article{arxiv.1302.1952,
title = {A converse to linear independence criteria, valid almost everywhere},
author = {Stéphane Fischler and Mumtaz Hussain and Simon Kristensen and Jason Levesley},
journal= {arXiv preprint arXiv:1302.1952},
year = {2013}
}