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A converse to linear independence criteria, valid almost everywhere

By S. Fischler, M. Hussain, S. Kristensen and J. Levesley
No. 01, March 2013
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.
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