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This is an introductory course to combinatorial number theory. The main objective of this course is to learn how to use combinatorial, topological, and analytic methods to solve problems in number the
Let (G/Γ, Ra) be an ergodic k-step nilsystem for k ≥ 2. We adapt an argument of Parry [Topology 9 (1970), pp. 217–224] to show that L2 (G/Γ) decomposes as a sum of a subspace with discrete spectrum and a subspace of Lebesgue spectrum with infinite multipli ...
. Originating in harmonic analysis, interpolation sets were first studied in dynamics by Glasner and Weiss in the 1980s [Israel J. Math. 44 (1983), pp. 345-360]. A set S subset of N is an interpolation set for a class of topological dynamical systems C if ...
We consider vanishing properties of exponential sums of the Liouville function λ of the form lim lim sup log1X mΣ≤X m1 sup α∈C|||| H1 Σ λ(m + h)e2πihα |||| = 0, H→∞ X→∞ h≤H where C ⊂ T. The case C = T corresponds to the local 1-Fourier uniformity conjectur ...
