3 papers
math.DS2026
Zero-one laws for uniform approximation via Gaussian and Eisenstein integers
René Pfitscher, Anurag Rao, Shucheng Yu +1
We establish two distinct zero-one laws for the uniform Diophantine approximation of complex numbers by quotients of Gaussian integers and by quotients of Eisenstein integers. Usin…
math.DS2025
Khintchine dichotomy and Schmidt estimates for self-similar measures on
Timothée Bénard, Weikun He, Han Zhang
We extend the classical theorems of Khintchine and Schmidt in metric Diophantine approximation to the context of self-similar measures on . For this, we establish eff…
math.DS2024
Khintchine dichotomy for self-similar measures
Timothée Bénard, Weikun He, Han Zhang
We establish the analogue of Khintchine's theorem for all self-similar probability measures on the real line. When specified to the case of the Hausdorff measure on the middle-thir…