7 papers · 1 filter
A short proof of Erdős's conjecture
Bryna Kra, Joel Moreira, Florian K. Richter +1
We give a short proof of the fact that every set of natural numbers with positive upper Banach density contains the sum of two infinite sets. The approach simplifies earlier existi…
A structure theorem for polynomial return-time sets in minimal systems
Daniel Glasscock, Andreas Koutsogiannis, Anh N. Le +3
We investigate the structure of return-time sets determined by orbits along polynomial tuples in minimal topological dynamical systems. Building on the topological characteristic f…
The Density Finite Sums Theorem
Bryna Kra, Joel Moreira, Florian K. Richter +1
For any set of natural numbers with positive upper Banach density and any , we show the existence of an infinite set and a shift such th…
Interpolation sets for dynamical systems
Andreas Koutsogiannis, Anh N. Le, Joel Moreira +2
Originating in harmonic analysis, interpolation sets were first studied in dynamics by Glasner and Weiss in the 1980s. A set is an interpolation set for a cl…
On the local Fourier uniformity problem for small sets
Adam Kanigowski, Mariusz Lemańczyk, Florian Karl Richter +1
We consider vanishing properties of exponential sums of the Liouville function of the form $$ \lim_{H\to\infty}\limsup_{X\to\infty}\frac{1}{\log X}\sum_{m\leq X}\frac{1}{m}\sup…
On the maximal spectral type of nilsystems
Ethan Ackelsberg, Florian K. Richter, Or Shalom
Let be an ergodic -step nilsystem for . We adapt an argument of Parry to show that decomposes as a sum of a subspace with discrete spectrum and a…