Kavita Dhanda

A geometric proof of Peck's theorem

Suppose that $d\ge 2$ and that $1,\alpha_1,\ldots ,\alpha_d$ is a basis for a real algebraic number field. A theorem of Peck from 1961 establishes that \[ \liminf_{n\rightarrow\infty}n\log n\,\|n\alpha_1\|\cdots\|n\alpha_d\|\<\infty.\] The goal of this paper is to recast Peck's proof in an intuitive geometric framework...