Inhomogeneous Khintchine-Groshev theorem without monotonicity
| Autor: | Kim, Seongmin |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The Khintchine-Groshev theorem in Diophantine approximation theory says that there is a dichotomy of the Lebesgue measure of sets of $\psi$-approximable numbers, given a monotonic function $\psi$. Allen and Ram\'irez removed the monotonicity condition from the inhomogeneous Khintchine-Groshev theorem for cases with $nm\geq3$ and conjectured that it also holds for $nm=2$. In this paper, we prove this conjecture in the case of $(n,m)=(2,1)$. We also prove it for the case of $(n,m)=(1,2)$ with a rational inhomogeneous parameter. Comment: 16 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|