Director of Research (if dissertation) or Advisor (if thesis)
Zaharescu, Alexandru
Doctoral Committee Chair(s)
Bruce, Berndt
Committee Member(s)
Hildebrand, A.J.
Zaharescu, Alexandru
Boca, Florin
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2013-08-22T16:48:59Z
Keyword(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.
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Jiajie_Xiao.pdf
