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Now showing items 31-40 of 66

#### 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 ...

#### Use-Bounded Strong Reducibilities

(University of Waterloo, 2009-08-20)

We study the degree structures of the strong reducibilities $(\leq_{ibT})$ and $(\leq_{cl})$, as well as $(\leq_{rK})$ and $(\leq_{wtt})$. We show that any noncomputable c.e. set is part of a uniformly c.e. copy of ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...