A uniform metrical theorem in multiplicative Diophantine approximation

Autor:	Björklund, Michael, Fregoli, Reynold, Gorodnik, Alexander
Rok vydání:	2022
Předmět:	Mathematics - Number Theory Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	For Lebesgue generic $(x_1,x_2)\in \mathbb{R}^2$, we investigate the distribution of small values of products $q\cdot \|qx_1\| \cdot \|qx_2\|$ with $q\in\mathbb{N}$, where $\|\cdot \|$ denotes the distance to the closest integer. The main result gives an asymptotic formula for the number of $1\le q\le T$ such that $$ a_T Comment: The Borel-Cantelli argument in the previous version is wrong, and has been corrected in the present version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.11593 Zobrazit plný text záznamu View this record from Arxiv