Random exponential sums and lattice points in regions

In this article we study two fundamental problems on exponential sums via randomization of frequencies with stochastic processes. These are the Hardy-Littlewood majorant problem, and $L^{2n}(\mathbb{T}), \ n\in \mathbb{N}$ norms of exponential sums, which can also be interpreted as solutions of diophantine equations or lattice points on surfaces. We establish connections to the well known problems on lattice points in regions such as the Dirichlet divisor problem.