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A converse to linear independence criteria, valid almost everywhere

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  • S. Fischler, Univ Paris 11, University of Paris Sud - Paris XI, Equipe Arithmet & Geometrie Algebr
  • ,
  • M. Hussain, Univ Newcastle, University of Newcastle, Sch Math & Phys Sci
  • ,
  • Simon Kristensen
  • J. Levesley, Univ York, University of York - UK, Dept Math

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 applied to proving the optimality of several linear independence criteria over the field of rational numbers.

OriginalsprogEngelsk
TidsskriftRamanujan Journal
Vol/bind38
Nummer3
Sider (fra-til)513-528
Antal sider16
ISSN1382-4090
DOI
StatusUdgivet - 2015

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