PhD Thesis Defence

Shuntaro Yamagishi, Pure Mathematics, University of Waterloo

"Some additive results in $\mathbb{F}_q[t]$"

We collected several results in $\mathbb{Z}$ of additive number theory and translated to results in $\mathbb{F}_q[t]$. The results we collected are related to slim exceptional sets and the asymptotic formula in Waring's problem, diophantine approximation of polynomials over $\mathbb{Z}$ satisfying  divisibility conditions, and the problem of Sidon regarding existence of certain thin sequences.