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math.DS2025
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…
math.CO2025
Sums and products in sets of positive density
Florian K. Richter
We develop an analytic approach that draws on tools from Fourier analysis and ergodic theory to study Ramsey-type problems involving sums and products in the integers. Suppose …
math.DS2025
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…