Browsing Mathematics (Faculty of) by Subject "Number theory"
Now showing items 1-4 of 4
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Applications of the minimal modelprogram in arithmetic dynamics
(University of Waterloo, 2021-09-07)Let F be a surjective endomorphism of a normal projective variety X defined over a number field. The dynamics of F may be studied through the dynamics of the linear action of an associated linear pull-back action on divisors. ... -
Generalizations of the Gap Principle and the Thue-Siegel Principle, with Applications to Diophantine Equations
(University of Waterloo, 2019-07-16)In this thesis we develop generalizations of two well-known principles from the theory of Diophantine approximation, namely the gap principle and the Thue-Siegel principle. Our results find their applications in the theory ... -
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 ...