5 problems

Let $\mathbb{K}$ be an arbitrary field and $P(t) \in \mathbb{K}[t]$ an irreducible polynomial over $\mathbb{K}$. For $\Gamma(t) \in \mathbb{K}((t^{-1}))$, write…

Let … Here $\|\cdot\|$ denotes the distance to the nearest integer. Conjecture that $\Theta_3$ is empty. The set $\Theta_3$ is the three-variable homogeneous analogue of the inhomo…

Uniform Littlewood conjecture. For any real numbers $xi,zeta$,

Let $x\in\mathbb{R}$, let $y>0$ be irrational, and let $\gamma\in\mathbb{R}$. For each positive integer $q$, write $\lVert\cdot\rVert$ for the distance to the nearest integer. Inho…

Logarithmically strengthened Littlewood conjecture. The Littlewood conjecture should hold in the strengthened form