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On a problem in simultaneous Diophantine approximation: Schmidt's conjecture

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JournalAnnals of Mathematics
DatePublished - Nov 2011
Issue number3
Volume174
Number of pages46
Pages (from-to)1837-1883
Original languageEnglish

Abstract

For any i,j≥0 with i+j=1 , let Bad(i,j) denote the set of points (x,y)∈R 2 for which max{∥qx∥ 1/i ,∥qy∥ 1/j }>c/q for all q∈N . Here c=c(x,y) is a positive constant. Our main result implies that any finite intersection of such sets has full dimension. This settles a conjecture of Wolfgang M. Schmidt in the theory of simultaneous Diophantine approximation.

    Research areas

  • Number Theory

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