Yamagishi, Shuntaro2015-08-272015-08-272015-08-272015http://hdl.handle.net/10012/9603We collected several results in integers of additive number theory and translated to results in F_q[t]. The results we collected are related to slim exceptional sets and the asymptotic formula in Waring's problem, a diophantine approximation of polynomials over integers satisfying divisibility conditions, and the problem of Sidon regarding the existence of certain thin sequences.enAdditive number theoryfunction fieldsDoctoral ThesisPure Mathematics