In this thesis, we consider several problems relating to cyclic subgroups of the group [mathematical equation]. Each element of [mathematical equation] has a unique representative in one of the two intervals [mathematical equation] and...
This thesis centers around a generalization of the classical discrete Fourier transform. We first present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite...
The study of twin primes gives rise to several famously difficult problems in number theory--in fact, we still cannot definitively say whether there are infinitely many twin primes. In this work, we consider a related problem, namely: What is the...
A polynomial is a product of distinct cyclotomic polynomials if and only if it is a divisor over [Special characters omitted.] [x ] of xn - 1 for some positive integer n. In this thesis, we will examine two natural questions concerning the divisors...