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Now showing items 21-30 of 38

#### On Convolution Squares of Singular Measures

(University of Waterloo, 2010-08-25)

We prove that if $1 > \alpha > 1/2$, then there exists a probability measure $\mu$ such that the Hausdorff dimension of its support is $\alpha$ and $\mu*\mu$ is a Lipschitz function of class $\alpha-1/2$.

#### Pick Interpolation and the Distance Formula

(University of Waterloo, 2012-05-09)

The classical interpolation theorem for the open complex unit disk, due to Nevanlinna and Pick in the early 20th century, gives an elegant criterion for the solvability of the problem as an eigenvalue problem. In the 1960s, ...

#### 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 ...

#### Contributions to the model theory of partial differential fields

(University of Waterloo, 2013-08-28)

In this thesis three topics on the model theory of partial differential fields are considered: the generalized Galois theory for partial differential fields, geometric axioms for the theory of partial differentially closed ...

#### Asymptotic Estimates for Rational Spaces on Hypersurfaces in Function Fields

(University of Waterloo, 2010-06-29)

The ring of polynomials over a finite field has many arithmetic properties similar to those of the ring of rational integers. In this thesis, we apply the Hardy-Littlewood circle method to investigate the density of rational ...

#### 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 ...

#### 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 ...

#### Semistable rank 2 co-Higgs bundles over Hirzebruch surfaces

(University of Waterloo, 2015-08-07)

It has been observed by S. Rayan that the complex projective surfaces that potentially
admit non-trivial examples of semistable co-Higgs bundles must be found at the lower end
of the Enriques-Kodaira classification. ...