Browsing by Author "Gilmore, Hamish Julian"

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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 ...
Computing L-Invariants for the Symmetric Square of an Elliptic Curve

Delbourgo, Daniel; Gilmore, Hamish Julian (Taylor & Francis, 2019)

Let E be an elliptic curve over Q, and p≠2 a prime of good ordinary reduction. The p-adic L-function for Sym²E always vanishes at s = 1, even though the complex L-function does not have a zero there. The L-invariant itself ...
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 ...