A converse to linear independence criteria, valid almost everywhere

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JournalThe Ramanujan Journal
DateE-pub ahead of print - 24 Jan 2015
DatePublished (current) - 2015
Number of pages11
Early online date24/01/15
Original languageEnglish

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.

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