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You searched for +publisher:"University of Illinois – Urbana-Champaign" +contributor:("Bruce, Berndt"). One record found.

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University of Illinois – Urbana-Champaign

1. Xiao, Jiajie. Distribution of some arithmetic sequences.

Degree: PhD, 0439, 2013, University of Illinois – Urbana-Champaign

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. Advisors/Committee Members: Zaharescu, Alexandru (advisor), Bruce, Berndt (Committee Chair), Hildebrand, A.J. (committee member), Zaharescu, Alexandru (committee member), Boca, Florin (committee member).

Subjects/Keywords: Number theory; analytic number theory.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Xiao, J. (2013). Distribution of some arithmetic sequences. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/45594

Chicago Manual of Style (16th Edition):

Xiao, Jiajie. “Distribution of some arithmetic sequences.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 19, 2019. http://hdl.handle.net/2142/45594.

MLA Handbook (7th Edition):

Xiao, Jiajie. “Distribution of some arithmetic sequences.” 2013. Web. 19 Jul 2019.

Vancouver:

Xiao J. Distribution of some arithmetic sequences. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2019 Jul 19]. Available from: http://hdl.handle.net/2142/45594.

Council of Science Editors:

Xiao J. Distribution of some arithmetic sequences. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/45594

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