Techniques from harmonic analysis play a crucial role in understanding problems in analytic number theory. For example, in 1916 Hermann Weyl initiated the study of the equidistribution of sequences on the additive circle, connecting fourier analysis to number theoretic dynamics.
Such techniques can be extended to other locally compact abelian groups, leading to some interesting number theory. We look at the p-adic unit ball as one such example. The talk is primarily intended to give a general mathematical audience a flavor and appreciation of this type of mathematics, and only a basic knowledge of analysis will be assumed.