On the rational approximation to linear combinations of powers

Veekesh Kumar, Gorekh Prasad

For a complex number $x$, $\Vert x\Vert :=\min \{|x-m|:m\in \mathbb{Z}\}$. Let $k\ge 1$ be an integer, and $K$ be a number field. Let $\hat{I}{\pm }_1,\dots ,\hat{I}{\pm }_k$ be algebraic numbers with $|Î…