2026-09-20T18:32:59Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/120085 2023-09-04 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Reznick, Bruce Zaharescu, Alexandru Berndt, Bruce C Nath, Kunjakanan 2023-05 application/pdf en text Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms The student, Grace Jaffe, accepted the attached license on 2023-04-23 at 20:17. The student, Grace Jaffe, submitted this Dissertation for approval on 2023-04-23 at 20:29. This Dissertation was approved for publication on 2023-04-28 at 09:08. DSpace SAF Submission Ingestion Package generated from Vireo submission #19123 on 2023-09-01 at 16:55:08 Topics in analytic number theory Jaffe, Grace Natalie 2023-04-28 Number Theory Frobenius Problem Stern Sequence Farey Sequences Dirichlet L-function Riemann Zeta Function In Part I of this thesis, we show that for relatively prime positive integers a,b, there is a maximum integer g(a,b) which is not expressible as ax+by for x,y non-negative, relatively prime integers. We then explore the connections between this quantity and the Frobenius problem, Farey sequence, and Stern sequence. In Part II, we consider the zeros of a polynomial in derivatives of a Dirichlet L-function and give an asymptotic formula for the number of zeros with imaginary part between 1 and large T. Thesis eng https://hdl.handle.net/2142/120085 Copyright 2023 Grace Jaffe Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics