Browsing Pure Mathematics by Title
Now showing items 72-91 of 165
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Intervals with few Prime Numbers
(University of Waterloo, 2004)In this thesis we discuss some of the tools used in the study of the number of primes in short intervals. In particular, we discuss a large sieve density estimate due to Gallagher and two classical delay equations. ... -
A k-Conjugacy Class Problem
(University of Waterloo, 2007-09-07)In any group G, we may extend the definition of the conjugacy class of an element to the conjugacy class of a k-tuple, for a positive integer k. When k = 2, we are forming the conjugacy classes of ordered pairs, when k ... -
K-theory for C*-Algebras and for Topological Spaces
(University of Waterloo, 2015-04-27)K-theory is the study of a collection of abelian groups that are invariant to C*-algebras or to locally compact Hausdorff spaces. These groups are useful for distinguishing C*-algebras and topological spaces, and they are ... -
Koblitz's Conjecture for the Drinfeld Module
(University of Waterloo, 2008-05-01)Let $E$ be an elliptic curve over the rationals without complex multiplication such that any elliptic curve $\mathbb{Q}$-isogenous to $E$ has trivial $\mathbb{Q}$-torsion. Koblitz conjectured that the number of primes less ... -
The Lang-Trotter conjecture for Drinfeld modules
(University of Waterloo, 2011-08-22)In 1986, Gupta and Murty proved the Lang-Trotter conjecture in the case of elliptic curves having complex multiplication, conditional on the generalized Riemann hypothesis. That is, given a non-torsion point P∈E(ℚ), they ... -
Lehmer Numbers with at Least 2 Primitive Divisors
(University of Waterloo, 2007-10-24)In 1878, Lucas \cite{lucas} investigated the sequences $(\ell_n)_{n=0}^\infty$ where $$\ell_n=\frac{\alpha^n-\beta^n}{\alpha-\beta},$$ $\alpha \beta$ and $\alpha+\beta$ are coprime integers, and where $\beta/\alpha$ is ... -
The Liftable Mapping Class Group
(University of Waterloo, 2017-07-19)Broadly, this thesis lies at the interface of mapping class groups and covering spaces. The foundations of this area were laid down in the early 1970s by Birman and Hilden. Building on these foundations, there has been a ... -
Linear preservers of polynomial numerical hulls of matrices
(Elsevier, 2019-08-15)Let Mn be the algebra of all n × n complex matrices, 1 ≤ k ≤ n − 1 be an integer, and φ : Mn −→ Mn be a linear operator. In this paper, it is shown that φ preserves the polynomial numerical hull of order k if and only if ... -
The Logarithmic Derivative and Model-Theoretic Analysability in Differentially Closed Fields
(University of Waterloo, 2019-01-22)This thesis deals with internal and analysable types, mainly in the context of the stable theory of differentially closed fields. Two main problems are dealt with: the construction of types analysable in the constants with ... -
A lower bound for the two-variable Artin conjecture and prime divisors of recurrence sequences
(Elsevier, 2019-01-01)In 1927, Artin conjectured that any integer other than −1 or a perfect square generates the multiplicative group (Z/pZ)× for infinitely many p. In 2000, Moree and Stevenhagen considered a two-variable version of this ... -
Lower order terms of moments of L-functions
(University of Waterloo, 2011-06-17)<p>Given a positive integer k, Conrey, Farmer, Keating, Rubinstein and Snaith conjectured a formula for the asymptotics of the k-th moments of the central values of quadratic Dirichlet L-functions. The conjectured formula ... -
MATRIX ALGEBRAS WITH A CERTAIN COMPRESSION PROPERTY I
(Elsevier, 2021-07-15)An algebra A of n × n complex matrices is said to be projection compressible if P AP is an algebra for all orthogonal projections P ∈ Mn(C). Analogously, A is said to be idempotent compressible if EAE is an algebra for all ... -
Maximal ideal space techniques in non-selfadjoint operator algebras
(University of Waterloo, 2013-04-26)The following thesis is divided into two main parts. In the first part we study the problem of characterizing algebras of functions living on analytic varieties. Specifically, we consider the restrictions M_V of the ... -
Maximal Operators in R^2
(University of Waterloo, 2007-08-13)A maximal operator over the bases $\mathcal{B}$ is defined as \[Mf(x) = \sup_{x \in B \in \mathcal{B}} \frac{1}{|B|}\int_B |f(y)|dy. \] The boundedness of this operator can be used in a number of applications including ... -
Mean Curvature Flow in Euclidean spaces, Lagrangian Mean Curvature Flow, and Conormal Bundles
(University of Waterloo, 2011-08-10)I will present the mean curvature flow in Euclidean spaces and the Lagrangian mean curvature flow. We will first study the mean curvature evolution of submanifolds in Euclidean spaces, with an emphasis on the case of ... -
Mind the GAP: Amenability Constants and Arens Regularity of Fourier Algebras
(University of Waterloo, 2023-08-28)This thesis aims to investigate properties of algebras related to the Fourier algebra $A(G)$ and the Fourier-Stieltjes algebra $B(G)$, where $G$ is a locally compact group. For a Banach algebra $\cA$ there are two natural ... -
The Model Theory of Algebraically Closed Fields
(University of Waterloo, 2000)Model theory can express properties of algebraic subsets of complex n-space. The constructible subsets are precisely the first order definable subsets, and varieties correspond to maximal consistent collections of ... -
Moment Polynomials for the Riemann Zeta Function
(University of Waterloo, 2009-01-21)In this thesis we calculated the coefficients of moment polynomials of the Riemann zeta function for k= 4, 5, 6...13 using cubic acceleration, which is an improved method from quadratic acceleration. We then numerically ... -
The Mordell-Lang Theorem from the Zilber Dichotomy
(University of Waterloo, 2010-04-30)We present a largely self-contained exposition of Ehud Hrushovski's proof of the function field Mordell-Lang conjecture beginning from the Zilber Dichotomy for differentially closed fields and separably closed fields. Our ... -
Multiplicities of Linear Recurrence Sequences
(University of Waterloo, 2006)In this report we give an overview of some of the major results concerning the multiplicities of linear recurrence sequences. We first investigate binary recurrence sequences where we exhibit a result due to Beukers and ...