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Author ORCID Identifier
N/A
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
Year Degree Awarded
2017
Month Degree Awarded
May
First Advisor
Siman Wong
Subject Categories
Number Theory
Abstract
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.
DOI
https://doi.org/10.7275/10008884.0
Recommended Citation
Nichols, Daniel, "Dynamical Systems and Zeta Functions of Function Fields" (2017). Doctoral Dissertations. 941.
https://doi.org/10.7275/10008884.0
https://scholarworks.umass.edu/dissertations_2/941