Diophantine approximation with restricted numerators and denominators on semisimple groups

Alexander Gorodnik; Shirali Kadyrov

doi:10.5802/jtnb.967

Diophantine approximation with restricted numerators and denominators on semisimple groups

Alexander Gorodnik, Shirali Kadyrov

Department of Mathematics

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

2 Citations (Scopus)

Abstract

We consider the problem of Diophantine approximation on semisimple algebraic groups by rational points with restricted numerators and denominators and establish a quantitative approximation result for all real points in the group by rational points with a prescribed denominator and an almost prime numerator.

Original language	English
Pages (from-to)	1-28
Number of pages	28
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	29
Issue number	1
DOIs	https://doi.org/10.5802/jtnb.967
Publication status	Published - 2017

Keywords

Almost primes
Diophantine approximation in algebraic groups
Property (τ)
Restricted diophantine approximation
Sieving on algebraic groups

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.5802/jtnb.967

Cite this

@article{82e6371c55274841a8323d65c83fde69,

title = "Diophantine approximation with restricted numerators and denominators on semisimple groups",

abstract = "We consider the problem of Diophantine approximation on semisimple algebraic groups by rational points with restricted numerators and denominators and establish a quantitative approximation result for all real points in the group by rational points with a prescribed denominator and an almost prime numerator.",

keywords = "Almost primes, Diophantine approximation in algebraic groups, Property (τ), Restricted diophantine approximation, Sieving on algebraic groups",

author = "Alexander Gorodnik and Shirali Kadyrov",

year = "2017",

doi = "10.5802/jtnb.967",

language = "English",

volume = "29",

pages = "1--28",

journal = "Journal de Theorie des Nombres de Bordeaux",

issn = "1246-7405",

publisher = "Universite de Bordeaux III (Michel de Montaigne)",

number = "1",

}

TY - JOUR

T1 - Diophantine approximation with restricted numerators and denominators on semisimple groups

AU - Gorodnik, Alexander

AU - Kadyrov, Shirali

PY - 2017

Y1 - 2017

N2 - We consider the problem of Diophantine approximation on semisimple algebraic groups by rational points with restricted numerators and denominators and establish a quantitative approximation result for all real points in the group by rational points with a prescribed denominator and an almost prime numerator.

AB - We consider the problem of Diophantine approximation on semisimple algebraic groups by rational points with restricted numerators and denominators and establish a quantitative approximation result for all real points in the group by rational points with a prescribed denominator and an almost prime numerator.

KW - Almost primes

KW - Diophantine approximation in algebraic groups

KW - Property (τ)

KW - Restricted diophantine approximation

KW - Sieving on algebraic groups

UR - http://www.scopus.com/inward/record.url?scp=85011798993&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85011798993&partnerID=8YFLogxK

U2 - 10.5802/jtnb.967

DO - 10.5802/jtnb.967

M3 - Article

AN - SCOPUS:85011798993

SN - 1246-7405

VL - 29

SP - 1

EP - 28

JO - Journal de Theorie des Nombres de Bordeaux

JF - Journal de Theorie des Nombres de Bordeaux

IS - 1

ER -

Diophantine approximation with restricted numerators and denominators on semisimple groups

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this