The local-global principle for integral Soddy sphere packings
The local-global principle for integral Soddy sphere packings
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DOI：
10.3934/jmd.2019019
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发表时间：
2012-08
影响因子：
1.1
通讯作者：
Alex Kontorovich
中科院分区：
文献类型：
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作者：
Alex Kontorovich
设K是P中所有曲率的集合，如果n在K中，也就是说，如果P中存在曲率等于n的球面，则称n为表示数。一个数n被称为容许数，如果它在任何地方都是局部表示的，这意味着对于所有q，n都在K（mod q）中。它表明，每一个足够大的容许数表示。
Fix an integral Soddy sphere packing P. Let K be the set of all curvatures in P. A number n is called represented if n is in K, that is, if there is a sphere in P with curvature equal to n. A number n is called admissible if it is everywhere locally represented, meaning that n is in K(mod q) for all q. It is shown that every sufficiently large admissible number is represented.