Electronic Theses and Dissertations

Date of Award


Document Type


Degree Name

Ph.D. in Mathematics

First Advisor

Thai Hoang Le

Second Advisor

Erwin Mina Diaz

Third Advisor

Rizwanur Khan


University of Mississippi

Relational Format



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.



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