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Now showing items 1-9 of 9

#### 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 ...

#### 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.

#### Amenability for the Fourier Algebra

(University of Waterloo, 2007-08-29)

The Fourier algebra A(G) can be viewed as a dual object for the group G and, in turn, for the group algebra L1(G). It is a commutative Banach algebra constructed using the representation theory of the group, and from which ...

#### 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.

#### A k-Conjugacy Class Problem

(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 ...

#### Maximal Operators in R^2

(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 ...

#### On Diagonal Acts of Monoids

(University of Waterloo, 2007-08-30)

In this paper we discuss what is known so far about diagonal acts of monoids. The first results that will be discussed comprise an overview of some work done on determining whether or not the diagonal act can be finitely ...

#### Posets of Non-Crossing Partitions of Type B and Applications

(University of Waterloo, 2007-10-19)

The thesis is devoted to the study of certain combinatorial
objects called \emph{non-crossing partitions}. The enumeration
properties of the lattice ${\textsf{NC$^{\textsf{\,A}}$(n)}}\,$ of
\emph{non-crossing partitions} ...