Bad(s, t) is hyperplane absolute winning

Erez Nesharim; David Simmons

doi:10.4064/aa164-2-4

Bad(s, t) is hyperplane absolute winning

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

Abstract

J. An proved that for any s,t ≥ 0 such that s+t=1, Bad (s,t)is (34√2)^-1-winning for Schmidt's game. We show that using the main lemma from [An] one can derive a stronger result, namely that Bad(s,t) is hyperplane absolute winning in the sense of [BFKRW]. As a consequence, one can deduce the full Hausdorff dimension of Bad(s,t) intersected with certain fractals.

Original language	English
Pages (from-to)	145-152
Number of pages	8
Journal	Acta Arithmetica
Volume	164
Issue number	2
DOIs	https://doi.org/10.4064/aa164-2-4
State	Published - 2014
Externally published	Yes

Keywords

Diophantine approximation
Schmidt's conjecture
Schmidt's game

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.4064/aa164-2-4

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title = "Bad(s, t) is hyperplane absolute winning",

abstract = "J. An proved that for any s,t ≥ 0 such that s+t=1, Bad (s,t)is (34√2)-1-winning for Schmidt's game. We show that using the main lemma from [An] one can derive a stronger result, namely that Bad(s,t) is hyperplane absolute winning in the sense of [BFKRW]. As a consequence, one can deduce the full Hausdorff dimension of Bad(s,t) intersected with certain fractals.",

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author = "Erez Nesharim and David Simmons",

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AU - Nesharim, Erez

AU - Simmons, David

N1 - Publisher Copyright: © Instytut Matematyczny PAN, 2014.

PY - 2014

Y1 - 2014

N2 - J. An proved that for any s,t ≥ 0 such that s+t=1, Bad (s,t)is (34√2)-1-winning for Schmidt's game. We show that using the main lemma from [An] one can derive a stronger result, namely that Bad(s,t) is hyperplane absolute winning in the sense of [BFKRW]. As a consequence, one can deduce the full Hausdorff dimension of Bad(s,t) intersected with certain fractals.

AB - J. An proved that for any s,t ≥ 0 such that s+t=1, Bad (s,t)is (34√2)-1-winning for Schmidt's game. We show that using the main lemma from [An] one can derive a stronger result, namely that Bad(s,t) is hyperplane absolute winning in the sense of [BFKRW]. As a consequence, one can deduce the full Hausdorff dimension of Bad(s,t) intersected with certain fractals.

KW - Diophantine approximation

KW - Schmidt's conjecture

KW - Schmidt's game

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U2 - 10.4064/aa164-2-4

DO - 10.4064/aa164-2-4

M3 - مقالة

SN - 0065-1036

VL - 164

SP - 145

EP - 152

JO - Acta Arithmetica

JF - Acta Arithmetica

IS - 2

ER -

Bad(s, t) is hyperplane absolute winning

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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