Two-dimensional badly approximable vectors and Schmidt's game
classification
🧮 math.NT
keywords
gameschmidtapproximablebadlytwo-dimensionalvectorsconjectureconsequence
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We prove that for any pair $(s,t)$ of nonnegative numbers with $s+t=1$, the set of two-dimensional $(s,t)$-badly approximable vectors is winning for Schmidt's game. As a consequence, we give a direct proof of Schmidt's conjecture using his game.
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