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Now showing items 1-10 of 27

#### 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 ...

#### 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 ...

#### Spectral Analysis of Laplacians on Certain Fractals

(University of Waterloo, 2007-12-06)

Surprisingly, Fourier series on certain fractals can have better
convergence properties than classical Fourier series. This is a
result of the existence of gaps in the spectrum of the Laplacian. In
this work we prove a ...

#### Digraph Algebras over Discrete Pre-ordered Groups

(University of Waterloo, 2013-01-25)

This thesis consists of studies in the separate fields of operator algebras and non-associative algebras. Two natural operator algebra structures, A ⊗_max B and A ⊗_min B, exist on the tensor product of two given unital ...

#### Some additive results in F_q[t]

(University of Waterloo, 2015-08-27)

We collected several results in integers of additive number theory and translated to results in F_q[t]. The results we collected are related to slim exceptional sets and the asymptotic formula in Waring's problem, a ...

#### Some aspects of Cantor sets

(University of Waterloo, 2014-03-28)

For every positive, decreasing, summable sequence $a=(a_i)$, we can construct a Cantor set $C_a$ associated with $a$. These Cantor sets are not necessarily self-similar. Their dimensional properties and measures have been ...

#### Higher-Dimensional Kloosterman Sums and the Greatest Prime Factor of Integers of the Form a_1a_2\cdots a_{k+1}+1

(University of Waterloo, 2007-08-29)

We consider the greatest prime factors of integers of certain form.

#### 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. ...

#### On a Question of Wintner Concerning the Sequence of Integers Composed of Primes from a Given Set

(University of Waterloo, 2007-09-27)

We answer to a Wintner's question
concerning the sequence of integers
composed of primes from a given set.
The results generalize and develop the answer to Wintner’s question due to
Tijdeman.

#### The Cohomology Ring of a Finite Abelian Group

(University of Waterloo, 2013-01-25)

The cohomology ring of a finite cyclic group was explicitly computed by Cartan and Eilenberg in their 1956 book on Homological Algebra. It is surprising that the cohomology ring for the next simplest example, that of a ...