Now showing items 76-95 of 165

    • The Lang-Trotter conjecture for Drinfeld modules 

      Tweedle, David (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 

      Juricevic, Robert (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 

      Ghaswala, Tyrone (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 

      Aghamollaei, Gh.; Marcoux, L.W.; Radjavi, H. (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 

      Jin, Ruizhang (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 

      Murty, M. Ram; Séguin, François; Stewart, Cameron L. (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 

      Rishikesh (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 

      Cramer, Zachary; Marcoux, Laurent W.; Radjavi, Heydar (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 

      Ramsey, Christopher (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 

      Choi, Keon (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 

      Leung, Chun Ho (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 

      Sawatzky, John (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 

      Cook, Daniel (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 

      Yamagishi, Shuntaro (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 

      Eagle, Christopher (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 

      Allen, Patrick (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 ...
    • Nevanlinna-Pick Spaces and Dilations 

      Hartz, Michael Peter (University of Waterloo, 2016-07-12)
      The majority of this thesis is devoted to the study of Nevanlinna-Pick spaces and their multiplier algebras. These spaces are Hilbert function spaces in which a version of the Nevanlinna-Pick interpolation theorem from ...
    • Non-Isotopic Symplectic Surfaces in Products of Riemann Surfaces 

      Hays, Christopher (University of Waterloo, 2006)
      <html> <head> <meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1"> </head> Let &Sigma;<em><sub>g</sub></em> be a closed Riemann surface of genus <em>g</em>. Generalizing Ivan Smith's construction, ...
    • The Normal Distribution of ω(φ(m)) in Function Fields 

      Li, Li (University of Waterloo, 2008-01-28)
      Let ω(m) be the number of distinct prime factors of m. A celebrated theorem of Erdös-Kac states that the quantity (ω(m)-loglog m)/√(loglog m) distributes normally. Let φ(m) be Euler's φ-function. Erdös and Pomerance ...
    • Normal operators with highly incompatible off-diagonal corners 

      Marcoux, Laurent W.; Radjavi, Heydar; Zhang, Yuanhang (Polish Academy of Sciences, 2020-05-25)
      Let H be a complex, separable Hilbert space, and B(H) denote the set of all bounded linear operators on H. Given an orthogonal projection P∈B(H) and an operator D∈B(H), we may write D=[D1D3D2D4] relative to the decomposition ...

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