Multiplicative Character Sums and the Applications to Problems in Analytic Number Theory
- Author(s): Castro, Kyle
- Advisor(s): Chang, Mei-Chu
- et al.
In this thesis, the reader is provided with a self-contained study of multiplicative characters
modulo composite integers. The results found here are primarily upper bounds on Dirichlet
characters, including those with polynomial arguments. Moreover, the applications of these
character sum bounds will also be discussed; in particular the direct impact on the lower
bound on the size of a subgroup of a finite field containing the image of an interval of
consecutive integers under a polynomial function is discussed in Chapter 4. My main goals
are to extend existing bounds on Dirichlet character sums to characters with composite
moduli and create new generalizations of character sums bounds while also providing the
reader with an understanding of the various applications.