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Author ORCID Identifier



Open Access Dissertation

Document Type


Degree Name

Doctor of Philosophy (PhD)

Degree Program


Year Degree Awarded


Month Degree Awarded


First Advisor

Siman Wong

Subject Categories

Number Theory


This doctoral dissertation concerns two problems in number theory. First, we examine a family of discrete dynamical systems in F_2[t] analogous to the 3x + 1 system on the positive integers. We prove a statistical result about the large-scale dynamics of these systems that is stronger than the analogous theorem in Z. We also investigate mx + 1 systems in rings of functions over a family of algebraic curves over F_2 and prove a similar result there. Second, we describe some interesting properties of zeta functions of algebraic curves. Generally L-functions vanish only to the order required by their root number. However, we demonstrate that for a certain class of quaternion extensions of F_p(t), the zeta function vanishes at a higher order than the root number demands, indicating some other phenomenon at work.


Included in

Number Theory Commons