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Title: Effective bisector estimate with application to Apollonian circle packings
Authors: Vinogradov, Ilya
Advisors: Sinai, Yakov G
Contributors: Mathematics Department
Keywords: Apollonian circle packings
bisector counting
hyperbolic lattice point counting
Subjects: Mathematics
Issue Date: 2012
Publisher: Princeton, NJ : Princeton University
Abstract: Let Gamma < PSL(2, C) be a geometrically finite non-elementary discrete subgroup, and let its critical exponent delta be greater than 1. We use representation theory of PSL(2, C) to prove an effective bisector counting theorem for Gamma, which allows counting the number of points of Gamma in general expanding regions in PSL(2, C) and provides an explicit error term. We apply this theorem to give power savings in the Apollonian circle packing problem and related counting problems.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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