In this dissertation, we use Fourier-analytic methods to study questions of equidistribution on the compact abelian group Zp of p-adic integers. In particu- lar, we prove a LeVeque-type Fourier analytic upper bound on the discrepancy of sequences. We establish p-adic analogues of the classical Dirichlet and Fejér kernels on R/Z,...
The standard way of representing numbers on computers gives rise to errors
which increase as computations progress. Using p-adic valuations can reduce
error accumulation. Valuation theory tells us that p-adic and standard valuations
cannot be directly compared. The p-adic valuation can, however, be used in
an indirect way. This gives...