12 papers
Weighted averages of arithmetic functions and applications to equidistribution and ergodic theory
Vitaly Bergelson, Michael Reilly, Florian K. Richter
For a wide range of functions , we establish a general result for estimating weighted averages of the form\[\mathbb{E}^{W}_{n \le N} f(\vartheta(n))…
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…
An inverse theorem for sumsets of sets of positive density in the integers
Ethan Ackelsberg, Florian K. Richter
Let denote the natural density on the positive integers. We characterize all sets with positive density satisfying , under the assumption that th…
No Constant-Cost Protocol for Point--Line Incidence
Mika Göös, Nathaniel Harms, Florian K. Richter +1
Alice and Bob are given -bit integer pairs and , respectively, and they must decide if . We prove that the randomised communication complexity of this Poi…
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…
Van der Waerden's theorem on arithmetic progressions -- a survey of some historical and modern developments
Vitaly Bergelson, Florian K. Richter
Van der Waerden's theorem, published in Nieuw. Arch. Wisk. 15 (1927), acted as a catalyst for major further developments in Ramsey theory. In this survey, we delve into the legacy…