Browsing by Supervisor "Delbourgo, Daniel"
Now showing items 14 of 4

Algebraic Properties of Chromatic Polynomials and Their Roots
(University of Waikato, 2015)In this thesis we examine chromatic polynomials from the viewpoint of algebraic number theory. We relate algebraic properties of chromatic polynomials of graphs to structural properties of those graphs for some simple ... 
Finding padic zeroes of the KubotaLeopoldt zetafunction numerically
(University of Waikato, 2014)We first establish why the padic zeta function has a Dirichlet series expansion. We then compute an improved expansion, which allows us to express it as a powerseries modulo pⁿ. Using this expansion, we compute all the ... 
Iwasawa theory over solvable threedimensional padic Lie extensions
(The University of Waikato, 2018)Iwasawa theory is a powerful tool which describes the mysterious relationship between arithmetic objects (motives) and the special values of Lfunctions. A precise form of this relationship is neatly encoded in the socalled ... 
Linvariants and congruences for Galois representations of dimension 3, 4, and 8
(The University of Waikato, 2020)The arithmetic of Galois representations plays a central role in modern number theory. In this thesis we consider representations arising from tensor products of the twodimensional representations attached to modular forms ...