Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp017d278t05z
 Title: Effective bisector estimate with application to Apollonian circle packings Authors: Vinogradov, Ilya Advisors: Sinai, Yakov G Contributors: Mathematics Department Keywords: Apollonian circle packingsbisector countinghyperbolic 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. URI: http://arks.princeton.edu/ark:/88435/dsp017d278t05z 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

Files in This Item:
File Description SizeFormat