# Browsing by Author "Delbourgo, Daniel"

Now showing items 1-5 of 17

• #### Algebraic invariants arising from the chromatic polynomials of theta graphs ﻿

(CMSA (Inc.), 2014)
This paper investigates some algebraic properties of the chromatic polynomials of theta graphs, i.e. graphs which have three internally disjoint paths sharing the same two distinct end vertices. We give a complete description ...
• #### Computing L-Invariants for the Symmetric Square of an Elliptic Curve ﻿

(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 ...
• #### Congruences modulo ρ between ρ-wisted Hasse-Weil L-values ﻿

(American Mathematical Society, 2018)
Suppose E₁ and E₂ are semistable elliptic curves over Q with good reduction at p, whose associated weight two newforms f₁ and f₂ have congruent Fourier coefficients modulo p. Let RS(E*, ρ) denote the algebraic padic L-value ...
• #### A conjecture of De Koninck regarding particular square values of the sum of divisors function ﻿

(Elsevier Inc, 2014)
We study integers n > 1 satisfying the relation σ(n) = γ(n)², where σ(n) and γ(n) are the sum of divisors and the product of distinct primes dividing n, respectively. If the prime dividing a solution n is congruent to 3 ...
• #### Corrigendum: A conjecture of De Koninck regarding particular values of the sum of divisors function ﻿

(Elsevier, 2017)
The proof of Lemma 7 of is made complete by giving the proof of a missing Case (4). This omission was pointed out to the authors by Min Tang, to whom we are most grateful. The same definitions and notation are employed ...

Daniel Delbourgo has 10 co-authors in Research Commons.

Showing up to 5 theses - most recently added to Research Commons first.

• #### L-invariants 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 two-dimensional representations attached to modular forms ...
• #### Iwasawa theory over solvable three-dimensional p-adic 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 L-functions. A precise form of this relationship is neatly encoded in the so-called ...
• #### 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 p-adic zeroes of the Kubota-Leopoldt zeta-function numerically ﻿

(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 ...