Distribution of some arithmetic sequences

Xiao, Jiajie

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Title:	Distribution of some arithmetic sequences
Author(s):	Xiao, Jiajie
Director of Research:	Zaharescu, Alexandru
Doctoral Committee Chair(s):	Bruce, Berndt
Doctoral Committee Member(s):	Hildebrand, A.J.; Zaharescu, Alexandru; Boca, Florin
Department / Program:	Mathematics
Discipline:	Mathematics
Degree Granting Institution:	University of Illinois at Urbana-Champaign
Degree:	Ph.D.
Genre:	Dissertation
Subject(s):	Number theory analytic number theory.
Abstract:	In this thesis, we first study the correlations of some arithmetic sequences. We prove the existence of the limiting pair correlations of fractions with prime and power denominators, and give the explicit pair correlation density functions. Next, we study the higher level correlations of these fractions, and construct an arithmetic sequence with showing the independence of its different level correlations. We also study the distribution of angles between common tangents of Ford circles, which is a special case of Apollonian circle packing. We provide the limiting distribution functions of these angles in different situations.
Issue Date:	2013-08-22
URI:	http://hdl.handle.net/2142/45594
Rights Information:	Copyright 2013 Jiajie Xiao
Date Available in IDEALS:	2013-08-22 2015-08-22
Date Deposited:	2013-08