On a problem in simultaneous Diophantine approximation: Schmidt's conjecture

Dzmitry Badziahin, Andrew Pollington, Sanju Velani

For any $i,j\ge 0$ with $i+j=1$, let $\bad(i,j)$ denote the set of points $(x,y)\in {\mathbb{R}}^2$ for which $\max \{\Vert qx{\Vert }^{1/i},\Vert qy{\Vert }^{1/j}\}>c/q$ for all $q\in \mathbb{N}$. Here $c…