Diagonal approximation in completions of Q

Matthew I Palmer

Diagonal approximation in completions of Q

Matthew I Palmer

Research output: Contribution to journal › Article (Academic Journal) › peer-review

2 Citations (Scopus)

Abstract

We prove analogues of some classical results from Diophantine approximation and metric number theory (namely Dirichlet's theorem and the Duffin–Schaeffer theorem) in the setting of diagonal Diophantine approximation, i.e. approximating elements of R×Q_p1×⋯×Q_pr by elements of the diagonal embedding of Q into this space.

Original language	English
Journal	Journal of Number Theory
Volume	147
Early online date	6 Sep 2014
Publication status	Published - Feb 2015

Keywords

Diophantine approximation
Metric number theory
Dirichlet's theorem
Duffin-Schaeffer theorem
Zero-one law
p-adic numbers

Handle.net

Persistent link

Cite this

@article{13a2d004c8624cddaacf75658a33f70b,

title = "Diagonal approximation in completions of Q",

abstract = "We prove analogues of some classical results from Diophantine approximation and metric number theory (namely Dirichlet's theorem and the Duffin–Schaeffer theorem) in the setting of diagonal Diophantine approximation, i.e. approximating elements of R×Qp1×⋯×Qpr by elements of the diagonal embedding of Q into this space.",

keywords = "Diophantine approximation, Metric number theory, Dirichlet's theorem, Duffin-Schaeffer theorem, Zero-one law, p-adic numbers",

author = "Palmer, {Matthew I}",

year = "2015",

month = feb,

language = "English",

volume = "147",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press",

}

TY - JOUR

T1 - Diagonal approximation in completions of Q

AU - Palmer, Matthew I

PY - 2015/2

Y1 - 2015/2

N2 - We prove analogues of some classical results from Diophantine approximation and metric number theory (namely Dirichlet's theorem and the Duffin–Schaeffer theorem) in the setting of diagonal Diophantine approximation, i.e. approximating elements of R×Qp1×⋯×Qpr by elements of the diagonal embedding of Q into this space.

AB - We prove analogues of some classical results from Diophantine approximation and metric number theory (namely Dirichlet's theorem and the Duffin–Schaeffer theorem) in the setting of diagonal Diophantine approximation, i.e. approximating elements of R×Qp1×⋯×Qpr by elements of the diagonal embedding of Q into this space.

KW - Diophantine approximation

KW - Metric number theory

KW - Dirichlet's theorem

KW - Duffin-Schaeffer theorem

KW - Zero-one law

KW - p-adic numbers

M3 - Article (Academic Journal)

VL - 147

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -

Diagonal approximation in completions of Q

Abstract

Keywords

Handle.net

Fingerprint

Cite this