Khintchine‐type theorems for weighted uniform inhomogeneous approximations via transference principle
Year: 2026
Type: article
Abstract: In 2019 Kleinbock and Wadleigh proved a “zero‐one law” for uniform inhomogeneous Diophantine approximations. We generalize this statement to arbitrary weight functions and establish a new and simple proof of this statement, based on the transference principle. We also give a complete description of the sets of ‐Dirichlet pairs with a fixed matrix in this setthe up from Lebesgue measure point of view. As an application, we consider the set of badly approximable matrices and give a characterization of bad approximability in terms of inhomogeneous approximations. All the aforementioned metrical descriptions work (and sometimes can be strengthened) for weighted Diophantine approximations.
Source: Mathematika
DOI: 10.1112/mtk.70089
Author: Vasiliy Neckrasov
Institution: Brandeis University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,930
OpenAlex ID: W4417101715
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