The Fuglede Conjecture Holds in
The Fuglede Conjecture Holds in
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富格莱德猜想成立
DOI：
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发表时间：
2019
影响因子：
0.5
通讯作者：
P. Birklbauer
中科院分区：
文献类型：
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作者：
P. Birklbauer
Fuglede猜想指出一个集合是谱的当且仅当它通过平移而平铺。该猜想被证伪陶维5及更高的一个反例，我们提出了一个计算机程序，确定了Fuglede猜想持有用尽搜索空间。最近Iosevich，Mayeli和Pakianathan表明，Fuglede猜想持有的主要领域时，维度不超过2。Aten等人先前针对p = 3解决了维度3的问题。在本文中，我们建立在Aten等人的结果之上，以允许计算机进行冗长的计算。
Abstract The Fuglede conjecture states that a set is spectral if and only if it tiles by translation. The conjecture was disproved by Tao for dimensions 5 and higher by giving a counterexample in We present a computer program that determines that the Fuglede conjecture holds in by exhausting the search space. Recently Iosevich, Mayeli and Pakianathan showed that the Fuglede conjecture holds over prime fields when the dimension does not exceed 2. The question for dimension 3 was previously addressed by Aten et al. for p = 3. In this paper we build upon those results by Aten et al. to allow a computer to carry out the lengthy computations.