An optimal bound for the ratio between ordinary and uniform exponents of Diophantine approximation

Antoine Marnat, Nikolay Moshchevitin

Research output: Working paperPreprint


We provide a lower bound for the ratio between the ordinary and uniform exponent of both simultaneous Diophantine approximation and Diophantine approximation by linear forms in any dimension. This lower bound was conjectured by Schmidt and Summerer and already shown in dimension $2$ and $3$. This lower bound is reached at regular systems presented in the context of parametric geometry of numbers, and thus optimal.
Original languageUndefined/Unknown
Publication statusPublished - 8 Feb 2018

Publication series e-Print archive
PublisherCornell University Library


  • math.NT

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