A converse to linear independence criteria, valid almost everywhere

Stéphane Fischler, Mumtaz Hussain, Simon Kristensen, Jason Levesley

Research output: Working paper/Preprint Working paperResearch

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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.
Original languageEnglish
PublisherDepartment of Mathematics, Aarhus University
Number of pages13
Publication statusPublished - 2013
SeriesPreprints
Number1
ISSN1397-4076

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