The local-global principle for integral soddy sphere packings

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Abstract

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 (Formula presented) 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 (Formula presented) B(mod q) for all q. It is shown that every sufficiently large admissible number is represented.

Original languageEnglish (US)
Pages (from-to)209-236
Number of pages28
JournalJournal of Modern Dynamics
Volume15
DOIs
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

Keywords

  • Arithmetic groups
  • Hyperbolic geometry
  • Local-global principle
  • Quadratic forms
  • Sphere packings
  • Thin groups

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