Rational approximation of affine coordinate subspaces of Euclidean space

Felipe A. Ramírez; David S. Simmons; Fabian Sueess

Rational approximation of affine coordinate subspaces of Euclidean space

Felipe A. Ramírez, David S. Simmons, Fabian Sueess

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that affine coordinate subspaces of dimension at least two in Euclidean space are of Khintchine type for divergence. For affine coordinate subspaces of dimension one, we prove a result which depends on the dual Diophantine type of the basepoint of the subspace. These results provide evidence for the conjecture that all affine subspaces of Euclidean space are of Khintchine type for divergence.

Original language	English
Journal	Acta Arithmetica
Early online date	2 Dec 2016
Publication status	Published - 2017

Bibliographical note

10 pages. v2: new introduction

Keywords

math.NT

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Rational approximation
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https://arxiv.org/abs/1510.05012

Programme Grant-New Frameworks in metric Number Theory
Velani, S. & Beresnevich, V.
EPSRC
1/06/12 → 30/11/18
Project: Research project (funded) › Research

Cite this

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AU - Sueess, Fabian

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AB - We show that affine coordinate subspaces of dimension at least two in Euclidean space are of Khintchine type for divergence. For affine coordinate subspaces of dimension one, we prove a result which depends on the dual Diophantine type of the basepoint of the subspace. These results provide evidence for the conjecture that all affine subspaces of Euclidean space are of Khintchine type for divergence.

KW - math.NT

M3 - Article

SN - 0065-1036

JO - Acta Arithmetica

JF - Acta Arithmetica

ER -

Rational approximation of affine coordinate subspaces of Euclidean space

Abstract

Bibliographical note

Keywords

Access to Document

Projects

Programme Grant-New Frameworks in metric Number Theory

Cite this