Ubiquitous systems and metric number theory

Arnaud Durand

We investigate the size and large intersection properties of $$E_t=\{x\in {\mathbb{R}}^d|\Vert x-k-x_i\Vert <{r_i}^t\text{for infinitely many}(i,k)\in I^{\mu ,\alpha }\times {\mathbb{Z}}^d\},$$ where $d\in\N…