Khintchine’s theorem on Diophantine approximation

Khintchine’s theorem on Diophantine approximation

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강연자 김성민
소속 서울대학교

Diophantine approximation is the study of approximating real numbers by rational numbers. For example, one can ask whether a real number x is ψ-approximable; that is, whether there are infinitely many rationals p/q satisfying |x-p/q|<ψ(q)/q for a given monotonic function ψ. A century ago, Khintchine discovered a remarkable dichotomy for the Lebesgue measure of the set of ψ-approximable numbers. Since then, Khintchine’s theorem has been extended in various directions, including inhomogeneous approximation and higher-dimensional generalizations. In this talk, I will introduce the Allen-Ramírez conjecture on removing the monotonicity condition from the inhomogeneous Khintchine-Groshev theorem and discuss a recent proof of the conjecture in the case (n,m)=(2,1).

음향문제로 강연 후반 음성이 출력되지 않습니다

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Now

현재 Khintchine’s theorem on Diophantine approximation

강연자 : 김성민 | 소속 : 서울대학교

Diophantine approximation is the study of approximating real numbers by rational numbers. For example, one can ask whether a real number x is ψ-approximable; that is, whether there are infinitely many rationals p/q satisfying |x-p/q|<ψ(q)/q for a given monotonic function ψ. A century ago, Khintchine discovered a remarkable dichotomy for the Lebesgue measure of the set of ψ-approximable numbers. Since then, Khintchine’s theorem has been extended in various directions, including inhomogeneous approximation and higher-dimensional generalizations. In this talk, I will introduce the Allen-Ramírez conjecture on removing the monotonicity condition from the inhomogeneous Khintchine-Groshev theorem and discuss a recent proof of the conjecture in the case (n,m)=(2,1).

음향문제로 강연 후반 음성이 출력되지 않습니다

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음향문제로 강연 시작 4분 후부터 음성이 출력됩니다.

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