Topics in analytic number theory

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2023

Author dc:creator

• Jaffe, Grace Natalie

Contributors dc:contributor

• Reznick, Bruce
• Zaharescu, Alexandru
• Berndt, Bruce C
• Nath, Kunjakanan

• Number Theory
• Frobenius Problem
• Stern Sequence
• Farey Sequences
• Dirichlet L-function
• Riemann Zeta Function

Statement dc:rights

• Copyright 2023 Grace Jaffe

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/120085

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F120085