论文标题
离散2D Cantor套件的分形不确定性
Fractal uncertainty for discrete 2D Cantor sets
论文作者
论文摘要
我们证明，在$ \ mathbb {z} _n \ times \ mathbb {z} _n $中设置的一个自相似的cantor设置为分形不确定性原理。我们证明中的关键要素是由于Ruppert和Beukers＆Smyth而导致Lang的猜想的定量形式。我们的定理回答了Dyatlov的问题，并具有打开量子图的应用。
We prove that a self-similar Cantor set in $\mathbb{Z}_N \times \mathbb{Z}_N$ has a fractal uncertainty principle if and only if it does not contain a pair of orthogonal lines. The key ingredient in our proof is a quantitative form of Lang's conjecture in number theory due to Ruppert and Beukers & Smyth. Our theorem answers a question of Dyatlov and has applications to open quantum maps.
