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Made available in DSpace on 2015-09-29T20:38:57Z (GMT). No. of bitstreams: 2 ROY-DISSERTATION-2015.pdf: 821854 bytes, checksum: 7abf6b7f9b1c512d8963ac66590c92b7 (MD5) LICENSE.txt: 4208 bytes, checksum: 502c6a39161a3e8620cd8507bf46885c (MD5) Previous issue date: 2015-08-03 application/pdf Zaharescu, Alexandru Berndt, Bruce C. Boca, Florin Athreya, Jayadev Roy, Arindam 2015-09-29T20:38:57Z 2015-09-29T20:38:57Z 2015-08 2015-08-03 Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-09-29 without embargo terms The student, Arindam Roy, accepted the attached license on 2015-07-30 at 14:49. The student, Arindam Roy, submitted this Dissertation for approval on 2015-07-30 at 14:49. This Dissertation was approved for publication on 2015-08-03 at 15:52. DSpace SAF Submission Ingestion Package generated from Vireo submission #8652 on 2015-09-29 at 13:23:44 http://hdl.handle.net/2142/88129 en Copyright 2015 Arindam Roy Ramanujan Voronoi summation formula Divisor problem Dedekind zeta function Dirichlet polynomial Distribution of zeros Hecke L-functions Approximate functional equation Proportion of zeros on the critical line Ramanujan's identities, Voronoi summation formula, and zeros of partial sums of zeta and L-functions text text 2015-8 Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.