A converse to linear independence criteria, valid almost everywhere

Stéphane Fischler (1) , Mumtaz Hussain (2) , Simon Kristensen (2) , Jason Levesley (3)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 Aarhus University [Aarhus]
3 University of York [York, UK]

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.

Domaines: Théorie des nombres [math.NT]

Stéphane Fischler, Mumtaz Hussain, Simon Kristensen, Jason Levesley. A converse to linear independence criteria, valid almost everywhere. Ramanujan Journal (The), 2015, 38, pp.513-528. ⟨hal-00786176⟩