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

Antoine Marnat; Nikolay Moshchevitin

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

Antoine Marnat, Nikolay Moshchevitin

Mathematics

Research output: Working paper › Preprint

Abstract

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 graph presented in the context of parametric geometry of numbers, and thus optimal.

Original language	English
Publication status	Published - 8 Feb 2018

Keywords

math.NT

Access to Document

1802.03081v1Other version, 263 KB

https://arxiv.org/abs/1802.03081

Cite this

@techreport{f0da7bd280294a938a5dc1f9f6c7f895,

title = "An optimal bound for the ratio between ordinary and uniform exponents of Diophantine approximation",

abstract = "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 graph presented in the context of parametric geometry of numbers, and thus optimal.",

keywords = "math.NT",

author = "Antoine Marnat and Nikolay Moshchevitin",

year = "2018",

month = feb,

day = "8",

language = "English",

type = "WorkingPaper",

}

TY - UNPB

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 graph 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 graph presented in the context of parametric geometry of numbers, and thus optimal.

KW - math.NT

M3 - Preprint

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

ER -