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oai:www.ideals.illinois.edu:2142/45594 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Zaharescu, Alexandru Bruce, Berndt Hildebrand, A.J. Zaharescu, Alexandru Boca, Florin Xiao, Jiajie 2013-08-22T16:48:59Z 2013-08-22T16:48:59Z 2015-08-22T10:00:47Z 2013-08 2013-08-22T16:48:59Z 2013-08 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-07-06T16:21:05Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Xiao_Jiajie.pdf: 478476 bytes, checksum: 2a4f15d67cf846ebd4f38aee162dcd04 (MD5) Made available in DSpace on 2013-08-22T16:48:59Z (GMT). No. of bitstreams: 2 Jiajie_Xiao.pdf: 478476 bytes, checksum: 2a4f15d67cf846ebd4f38aee162dcd04 (MD5) license.txt: 4058 bytes, checksum: e3338024786221a632c36d44d831ca3b (MD5) Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Seth Robbins (srobbins@illinois.edu) on 2013-08-22T16:49:44Z Item is restricted until 2015-08-22T16:49:27Z Restriction data tranferred 2014-07-01T11:34:23-05:00 Original Data Group with Access UIUC Users [automated] Release Date: 2015-08-22 11:49:27 UTC Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only Restriction Lifted for Item 45576 on 2015-08-22T10:00:47Z. http://hdl.handle.net/2142/45594 en Copyright 2013 Jiajie Xiao Number theory analytic number theory. Distribution of some arithmetic sequences text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD