Diophantine Approximation and applications in Interference Alignment

Faustin Adiceam; Victor Beresnevich; Jason Levesley; Sanju Velani; Evgeniy Zorin

doi:10.1016/j.aim.2016.07.002

Diophantine Approximation and applications in Interference Alignment

Faustin Adiceam, Victor Beresnevich, Jason Levesley, Sanju Velani, Evgeniy Zorin

Mathematics

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

Abstract

This paper is motivated by recent applications of Diophantine approximation in electronics, in particular, in the rapidly developing area of Interference Alignment. Some remarkable advances in this area give substantial credit to the fundamental Khintchine-Groshev Theorem and, in particular, to its far reaching generalisation for submanifolds of a Euclidean space. With a view towards the aforementioned applications, here we introduce and prove quantitative explicit generalisations of the Khintchine-Groshev Theorem for non-degenerate submanifolds of R ⁿ. The importance of such quantitative statements is explicitly discussed in Jafar's monograph [12, §4.7.1].

Original language	English
Pages (from-to)	231-279
Number of pages	49
Journal	Advances in Mathematics
Volume	302
Early online date	27 Jul 2016
DOIs	https://doi.org/10.1016/j.aim.2016.07.002
Publication status	Published - 22 Oct 2016

Bibliographical note

Keywords

Khintchine-Groshev Theorem
Metric Diophantine approximation
Non-degenerate manifolds

Access to Document

10.1016/j.aim.2016.07.002Licence: CC BY

1-s2.0-S0001870816308659-main
©2016 The Author(s). Published by Elsevier Inc
Final published version, 599 KBLicence: CC BY

Cite this

@article{5cd248305c764e4b81d0d2b27e4ae287,

title = "Diophantine Approximation and applications in Interference Alignment",

abstract = "This paper is motivated by recent applications of Diophantine approximation in electronics, in particular, in the rapidly developing area of Interference Alignment. Some remarkable advances in this area give substantial credit to the fundamental Khintchine-Groshev Theorem and, in particular, to its far reaching generalisation for submanifolds of a Euclidean space. With a view towards the aforementioned applications, here we introduce and prove quantitative explicit generalisations of the Khintchine-Groshev Theorem for non-degenerate submanifolds of R n. The importance of such quantitative statements is explicitly discussed in Jafar's monograph [12, §4.7.1]. ",

keywords = "Khintchine-Groshev Theorem, Metric Diophantine approximation, Non-degenerate manifolds",

author = "Faustin Adiceam and Victor Beresnevich and Jason Levesley and Sanju Velani and Evgeniy Zorin",

note = "{\textcopyright}2016 The Author(s). Published by Elsevier Inc",

year = "2016",

month = oct,

day = "22",

doi = "10.1016/j.aim.2016.07.002",

language = "English",

volume = "302",

pages = "231--279",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press",

}

TY - JOUR

T1 - Diophantine Approximation and applications in Interference Alignment

AU - Adiceam, Faustin

AU - Beresnevich, Victor

AU - Levesley, Jason

AU - Velani, Sanju

AU - Zorin, Evgeniy

PY - 2016/10/22

Y1 - 2016/10/22

N2 - This paper is motivated by recent applications of Diophantine approximation in electronics, in particular, in the rapidly developing area of Interference Alignment. Some remarkable advances in this area give substantial credit to the fundamental Khintchine-Groshev Theorem and, in particular, to its far reaching generalisation for submanifolds of a Euclidean space. With a view towards the aforementioned applications, here we introduce and prove quantitative explicit generalisations of the Khintchine-Groshev Theorem for non-degenerate submanifolds of R n. The importance of such quantitative statements is explicitly discussed in Jafar's monograph [12, §4.7.1].

AB - This paper is motivated by recent applications of Diophantine approximation in electronics, in particular, in the rapidly developing area of Interference Alignment. Some remarkable advances in this area give substantial credit to the fundamental Khintchine-Groshev Theorem and, in particular, to its far reaching generalisation for submanifolds of a Euclidean space. With a view towards the aforementioned applications, here we introduce and prove quantitative explicit generalisations of the Khintchine-Groshev Theorem for non-degenerate submanifolds of R n. The importance of such quantitative statements is explicitly discussed in Jafar's monograph [12, §4.7.1].

KW - Khintchine-Groshev Theorem

KW - Metric Diophantine approximation

KW - Non-degenerate manifolds

UR - http://www.scopus.com/inward/record.url?scp=84979619714&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2016.07.002

DO - 10.1016/j.aim.2016.07.002

M3 - Article

SN - 0001-8708

VL - 302

SP - 231

EP - 279

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Diophantine Approximation and applications in Interference Alignment

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Jason Levesley

Programme Grant-New Frameworks in metric Number Theory

Cite this

Diophantine Approximation and applications in Interference Alignment

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Profiles

Jason Levesley

Projects

Programme Grant-New Frameworks in metric Number Theory

Cite this