Browsing by Supervisor "Delbourgo, Daniel"

Now showing items 1-4 of 4

  • Algebraic Properties of Chromatic Polynomials and Their Roots

    Gilmore, Hamish Julian (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 p-adic zeroes of the Kubota-Leopoldt zeta-function numerically

    Alharbi, Nof Turki S (University of Waikato, 2014)
    We first establish why the p-adic zeta function has a Dirichlet series expansion. We then compute an improved expansion, which allows us to express it as a power-series modulo pⁿ. Using this expansion, we compute all the ...

  • Iwasawa theory over solvable three-dimensional p-adic Lie extensions

    Qin, Chao (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 L-functions. A precise form of this relationship is neatly encoded in the so-called ...

  • L-invariants and congruences for Galois representations of dimension 3, 4, and 8

    Gilmore, Hamish Julian (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 two-dimensional representations attached to modular forms ...