博雅讲座之二： The measure and fractal properties of Dirichlet non-improvable sets

讲座时间：2021年9月20日(周一)下午3:40-4:40

讲座专家：吴军教授，华中科技大学

Abstract：Dirichlet’s theorem is a fundamental result in metric Diophantine approximation. The improvability of this theorem was first considered by Davenport andSchmidt. After them, Kleinbock and Wadleigh proposed the concept of Dirichlet improvable point formally in 2018 and launched relevant work. Their resultsshow that the improvability of Dirichlet’s theorem is concerned with the growthof the product of the partial quotients.In this talk, we present some results on the size of uniformly Dirichlet non-improvable set, the size of exact Dirichlet non-improvable set and metric properties of the product of the partial quotients in continued fractions.

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