Distribution of some arithmetic sequences

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2013

Author dc:creator

• Xiao, Jiajie

Contributors dc:contributor

• Zaharescu, Alexandru
• Bruce, Berndt
• Hildebrand, A.J.
• Boca, Florin

• Number theory
• analytic number theory.

Statement dc:rights

• Copyright 2013 Jiajie Xiao

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/45594

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/45594