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Now showing items 1-9 of 9

#### Artin's Conjecture: Unconditional Approach and Elliptic Analogue

(University of Waterloo, 2008-08-11)

In this thesis, I have explored the different approaches towards proving Artin's
`primitive root' conjecture unconditionally and the elliptic curve analogue of the
same. This conjecture was posed by E. Artin in the year ...

#### The Normal Distribution of ω(φ(m)) in Function Fields

(University of Waterloo, 2008-01-28)

Let ω(m) be the number of distinct prime factors of m. A
celebrated theorem of Erdös-Kac states that the quantity
(ω(m)-loglog m)/√(loglog m) distributes
normally. Let φ(m) be Euler's φ-function. Erdös and
Pomerance ...

#### Operator Spaces and Ideals in Fourier Algebras

(University of Waterloo, 2008-08-11)

In this thesis we study ideals in the Fourier algebra, A(G), of a
locally compact group G.
For a locally compact abelian group G, necessary conditions for a
closed ideal in A(G) to be weakly complemented are given, ...

#### Branched Covering Constructions and the Symplectic Geography Problem

(University of Waterloo, 2008-08-15)

We apply branched covering techniques to construct minimal simply-connected symplectic 4-manifolds with small χ_h values. We also use these constructions to provide an alternate proof that for each s ≥ 0, there exists a ...

#### A Survey of the Classification of Division Algebras

(University of Waterloo, 2008-09-29)

For a given field F we seek all division algebras over F up to isomorphism. This question was first investigated for division algebras of finite dimension over F by Richard Brauer. We discuss the construction of the Brauer ...

#### Koblitz's Conjecture for the Drinfeld Module

(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 ...

#### Artin's Primitive Root Conjecture and its Extension to Compositie Moduli

(University of Waterloo, 2008-08-11)

If we fix an integer a not equal to -1 and which is not a perfect square, we are interested in estimating the quantity N_{a}(x) representing the number of prime integers p up to x such that a is a generator of the cyclic ...

#### Von Neumann Algebras for Abstract Harmonic Analysis

(University of Waterloo, 2008-08-28)

This thesis develops the theory of operator algebras from the perspective of abstract harmonic analysis, and in particular, the theory of von Neumann algebras. Results from operator algebras are applied to the study of ...

#### The Weil conjectures

(University of Waterloo, 2008-01-24)

In discussing the question of rational points on algebraic curves, we are usually concerned with ℚ. André Weil looked instead at curves over finite fields; assembling the counts into a function, he discovered that it ...