THE LOCAL-GLOBAL PRINCIPLE FOR INTEGRAL SODDY SPHERE PACKINGS

被引：2
|
作者：
Kontorovich, Alex [1 ]
机构：
[1] Rutgers State Univ, Dept Math, 110 Frelinghuysen Rd, Piscataway, NJ 08854 USA
来源：
JOURNAL OF MODERN DYNAMICS | 2019年 / 15卷
关键词：
Sphere packings; thin groups; hyperbolic geometry; arithmetic groups; quadratic forms; local-global principle; APOLLONIAN CIRCLE PACKINGS; GEOMETRY;
D O I：
10.3934/jmd.2019019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Fix an integral Soddy sphere packing P. Let B be the set of all bends in P. A number n is called represented if n is an element of B, that is, if there is a sphere in P with bend equal to n. A number n is called admissible if it is everywhere locally represented, meaning that n is an element of B(mod q) for all q. It is shown that every sufficiently large admissible number is represented.
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页码：209 / 236
页数：28
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