Now showing items 65-84 of 165

    • Harmonic analysis of Rajchman algebras 

      Ghandehari, Mahya (University of Waterloo, 2010-08-31)
      Abstract harmonic analysis is mainly concerned with the study of locally compact groups, their unitary representations, and the function spaces associated with them. The Fourier and Fourier-Stieltjes algebras are two of ...
    • Higher-Dimensional Kloosterman Sums and the Greatest Prime Factor of Integers of the Form a_1a_2\cdots a_{k+1}+1 

      Wu, Shengli (University of Waterloo, 2007-08-29)
      We consider the greatest prime factors of integers of certain form.
    • Hilbert space operators with compatible off-diagonal corners 

      Livshits, Leo; MacDonald, Gordon; Marcoux, Laurent W.; Radjavi, Heydar (Elsevier, 2018-08-15)
      Given a complex, separable Hilbert space H, we characterize those operators for which ‖PT(I−P)‖=‖(I−P)TP‖ for all orthogonal projections P on H. When H is finite-dimensional, we also obtain a complete characterization of ...
    • Infinite Sets of D-integral Points on Projective Algebrain Varieties 

      Shelestunova, Veronika (University of Waterloo, 2005)
      Let <em>X</em>(<em>K</em>) &sub; <strong>P</strong><sup><em>n</em></sup> (<em>K</em>) be a projective algebraic variety over <em>K</em>, and let <em>D</em> be a subset of <strong>P</strong><sup><em>n</em></sup><sub><em>O ...
    • Integral Moments of Quadratic Dirichlet L-functions: A Computational Perspective 

      Alderson, Matthew (University of Waterloo, 2010-04-27)
      In recent years, the moments of L-functions has been a topic of growing interest in the field of analytic number theory. New techniques, including applications of Random Matrix Theory and multiple Dirichlet series, have ...
    • Integrality theorems for symmetric instantons 

      Whitehead, Spencer (University of Waterloo, 2022-08-05)
      Anti-self-dual (ASD) instantons on R4 are connections A on SU(N)-vector bundles with finite L2-norm and curvature satisfying the ASD equation. Solutions to this non-linear partial differential equation correspond to certain ...
    • Interpolation Sets For Compact Abelian Groups 

      Yang, Xu (University of Waterloo, 2014-09-04)
      We will study various properties of I_0 and \epsilon-Kronecker sets. We show that most infinite sets in the discrete dual group contain infinite interpolation sets.
    • Intervals with few Prime Numbers 

      Wolczuk, Dan (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 

      Roberts, Collin (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 

      Xiao, Rui Philip (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 

      Jain, Lalit Kumar (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 

      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 ...

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