Hausdorff measure of sets of inhomogeneous Dirichlet non-improvable affine forms with weights

2025/05/22 by Yubin He, He, Yubin · 1 citation
Mathematics · #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2505.16473

openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Under a reasonable decay assumption on the approximating function, we establish a zero-full law for the Hausdorff measure of sets of inhomogeneous Dirichlet non-improvable affine forms with weights, thereby answering a question posed by Kim and Kim (§5.3, Adv. Math., 2022).

Citations

• Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation
• Diophantine approximation and the Mass Transference Principle: incorporating the unbounded setup
• A unified approach to mass transference principle and large intersection property
• A measure estimate in geometry of numbers and improvements to Dirichlet's theorem
• Mass transference principle from rectangles to rectangles in Diophantine approximation
• Mass transference principle: from balls to arbitrary shapes
• A zero-one Law for improvements to Dirichlet's Theorem

Cited by

• Khintchine-type theorems for weighted uniform inhomogeneous approximations via transference principle

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