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Ford, Kevin Ahlgren, Scott Berndt, Bruce Zaharescu, Alexandru Pratt, Kyle 2019-08-23T19:51:50Z 2019-08-23T19:51:50Z 2019-04-12 2019-05 We investigate properties of prime numbers and L-functions, and interactions between these two topics. First, we discuss the problem of primes in thin sequences, expanding on work of Maynard and Friedlander-Iwaniec. Next, motivated by work of Iwaniec and Sarnak, we study the question of average nonvanishing of Dirichlet L-functions at the central point. Finally, in joint work with Siegfred Baluyot, we build on work of Soundararajan and synthesize our studies of primes and L-functions by examining Dirichlet L-functions of quadratic characters of prime conductor. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-08-22 without embargo terms The student, Kyle Pratt, accepted the attached license on 2019-04-12 at 10:02. The student, Kyle Pratt, submitted this Dissertation for approval on 2019-04-12 at 10:08. This Dissertation was approved for publication on 2019-04-12 at 13:30. DSpace SAF Submission Ingestion Package generated from Vireo submission #13581 on 2019-08-22 at 14:43:08 Made available in DSpace on 2019-08-23T19:51:50Z (GMT). No. of bitstreams: 2 PRATT-DISSERTATION-2019.pdf: 1082490 bytes, checksum: 6e50cd9241941d6b1fccf8dc144f2d79 (MD5) LICENSE.txt: 4207 bytes, checksum: 0131478ba8572a39ce96b92584d59834 (MD5) Previous issue date: 2019-04-12 application/pdf http://hdl.handle.net/2142/104815 en Copyright 2019 Kyle Pratt prime numbers Dirichlet L-functions Topics in analytic number theory text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.