Date of Award
1-1-2020
Document Type
Dissertation
Degree Name
Ph.D. in Mathematics
First Advisor
Thai Hoang Le
Second Advisor
Erwin Mina Diaz
Third Advisor
Rizwanur Khan
School
University of Mississippi
Relational Format
dissertation/thesis
Abstract
In this dissertation, I introduce some results that I have proved (collaboratively and independently) in analytic number theory and additive combinatorics. In analytic number theory, I study certain continuous and discrete mean value estimates for the Z-function associated to a Dirichlet L-functions. These problems lead naturally to an investigation of certain Gauss type sums which are studied in some depth. This is joint work with Jonathan W. Bober and Micah B. Milinovich. In additive combinatorics, I study two problems on sumsets. This is joint work with Thai Hoang Le.
Recommended Citation
Ge, Zhenchao, "Topics In Analytic And Combinatorial Number Theory" (2020). Electronic Theses and Dissertations. 1891.
https://egrove.olemiss.edu/etd/1891