@techreport{a5b721a46adc410e99b6ce05faef37e8,

title = "A converse to linear independence criteria, valid almost everywhere",

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.",

author = "St{\'e}phane Fischler and Mumtaz Hussain and Simon Kristensen and Jason Levesley",

year = "2013",

language = "English",

series = "Preprints",

publisher = "Department of Mathematics, Aarhus University",

number = "1",

type = "WorkingPaper",

institution = "Department of Mathematics, Aarhus University",

}