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Now showing items 21-30 of 38

#### On the Erdös-Turán conjecture and related results

(University of Waterloo, 2011-08-29)

The Erdös-Turán Conjecture, posed in 1941 in, states that if a subset B of natural numbers is such that every positive integer n can be written as the sum of a bounded number of terms from B, then the number of such ...

#### A survey of Roth's Theorem on progressions of length three

(University of Waterloo, 2011-12-19)

For any finite set B and a subset A⊆B, we define the density of A in B to be the value α=|A|/|B|. Roth's famous theorem, proven in 1953, states that there is a constant C>0, such that if A⊆{1,...,N} for a positive integer ...

#### 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 ...

#### Integral Moments of Quadratic Dirichlet L-functions: A Computational Perspective

(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 ...

#### 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 ...

#### Representations of Operator Algebras

(University of Waterloo, 2012-05-11)

The following thesis is divided into two main chapters. In Chapter 2 we study isometric representations of product systems of correspondences over the semigroup 𝐍ᵏ which are minimal dilations of finite dimensional, fully ...

#### Interpolation Sets For Compact Abelian Groups

(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.

#### Free semigroup algebras and the structure of an isometric tuple

(University of Waterloo, 2011-06-28)

An n-tuple of operators V=(V_1,…,V_n) acting on a Hilbert space H is said to be isometric if the corresponding row operator is an isometry. A free semigroup algebra is the weakly closed algebra generated by an isometric ...

#### Families of Thue Inequalities with Transitive Automorphisms

(University of Waterloo, 2014-06-17)

A family of parameterized Thue equations is defined as F_{t,s,...}(X, Y ) = m, m ∈ Z
where F_{t,s,...}(X,Y) is a form in X and Y with degree greater than or equal to 3 and integer coefficients that are parameterized by ...

#### Settling Time Reducibility Orderings

(University of Waterloo, 2010-04-28)

It is known that orderings can be formed with settling time domination and strong settling time domination as relations on c.e. sets. However, it has been shown that no such ordering can be formed when considering computation ...