Badly approximable affine forms and Schmidt games

Jimmy Tseng

doi:10.1016/j.jnt.2009.05.006

Badly approximable affine forms and Schmidt games

Jimmy Tseng^*

^*Corresponding author for this work

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

26 Citations (Scopus)

Abstract

For any real number Θ, the set of all real numbers x for which there exists a constant c(x) > 0 such that inf _p∈(|Θq - x- p|≥ c(x)/|q| for all p∈(\{0} is a 1/8-winning set.

Original language	English
Pages (from-to)	3020-3025
Number of pages	6
Journal	Journal of Number Theory
Volume	129
Issue number	12
DOIs	https://doi.org/10.1016/j.jnt.2009.05.006
Publication status	Published - Dec 2009

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title = "Badly approximable affine forms and Schmidt games",

abstract = "For any real number Θ, the set of all real numbers x for which there exists a constant c(x) > 0 such that inf p∈(|Θq - x- p|≥ c(x)/|q| for all p∈(\textbackslash{}\{0\} is a 1/8-winning set.",

author = "Jimmy Tseng",

year = "2009",

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doi = "10.1016/j.jnt.2009.05.006",

language = "English",

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journal = "Journal of Number Theory",

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T1 - Badly approximable affine forms and Schmidt games

AU - Tseng, Jimmy

PY - 2009/12

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N2 - For any real number Θ, the set of all real numbers x for which there exists a constant c(x) > 0 such that inf p∈(|Θq - x- p|≥ c(x)/|q| for all p∈(\{0} is a 1/8-winning set.

AB - For any real number Θ, the set of all real numbers x for which there exists a constant c(x) > 0 such that inf p∈(|Θq - x- p|≥ c(x)/|q| for all p∈(\{0} is a 1/8-winning set.

UR - https://www.scopus.com/pages/publications/77958554797

U2 - 10.1016/j.jnt.2009.05.006

DO - 10.1016/j.jnt.2009.05.006

M3 - Article (Academic Journal)

AN - SCOPUS:77958554797

SN - 0022-314X

VL - 129

SP - 3020

EP - 3025

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 12

ER -

Badly approximable affine forms and Schmidt games

Abstract

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