### Abstract

Original language | Undefined/Unknown |
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Journal | arXiv.org e-Print archive |

Publication status | Published - 8 Feb 2018 |

### Keywords

- math.NT

### Cite this

**An optimal bound for the ratio between ordinary and uniform exponents of Diophantine approximation.** / Marnat, Antoine; Moshchevitin, Nikolay.

Research output: Contribution to journal › Article › Research

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TY - JOUR

T1 - An optimal bound for the ratio between ordinary and uniform exponents of Diophantine approximation

AU - Marnat, Antoine

AU - Moshchevitin, Nikolay

PY - 2018/2/8

Y1 - 2018/2/8

N2 - 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.

AB - 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.

KW - math.NT

M3 - Artikel

JO - arXiv.org e-Print archive

JF - arXiv.org e-Print archive

ER -