3 problems

Inhomogeneous Gallagher divergence conjecture. If

Cassels' logarithmic conjecture. Almost every pair $(x_1,x_2)\in\mathbb{R}^2$ satisfies, for every $(\gamma_1,\gamma_2)\in\mathbb{R}^2$,

Logarithmic Littlewood conjecture. For every pair $(\alpha,\beta)\in\mathbb{R}^2$,